5,258 results on '"ORNSTEIN-Uhlenbeck process"'
Search Results
2. Efficient Langevin and Monte Carlo sampling algorithms: The case of field-theoretic simulations.
- Author
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Vorselaars, Bart
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ORNSTEIN-Uhlenbeck process , *ALGORITHMS - Abstract
We introduce Langevin sampling algorithms to field-theoretic simulations (FTSs) of polymers that, for the same accuracy, are ∼10× more efficient than a previously used Brownian dynamics algorithm that used predictor corrector for such simulations, over 10× more efficient than the smart Monte Carlo (SMC) algorithm, and typically over 1000× more efficient than a simple Monte Carlo (MC) algorithm. These algorithms are known as the Leimkuhler–Matthews (the BAOAB-limited) method and the BAOAB method. Furthermore, the FTS allows for an improved MC algorithm based on the Ornstein–Uhlenbeck process (OU MC), which is 2× more efficient than SMC. The system-size dependence of the efficiency for the sampling algorithms is presented, and it is shown that the aforementioned MC algorithms do not scale well with system sizes. Hence, for larger sizes, the efficiency difference between the Langevin and MC algorithms is even greater, although, for SMC and OU MC, the scaling is less unfavorable than for the simple MC. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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3. Harnack inequalities for functional SDEs driven by subordinate Volterra-Gaussian processes.
- Author
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Xu, Liping, Yan, Litan, and Li, Zhi
- Subjects
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FUNCTIONAL differential equations , *BROWNIAN motion , *ORNSTEIN-Uhlenbeck process , *STOCHASTIC difference equations , *STOCHASTIC differential equations , *FRACTIONAL differential equations - Abstract
Based on the Girsanov theorem for a kind of Volterra-Gaussian process, which are the generalization of fractional Brownian motion, Liouville fractional Brownian motion, and fractional Ornstein-Uhlenbeck process, we establish the Harnack inequalities for a class of stochastic functional differential equations driven by a kind of Volterra-Gaussian processes with a subordinator by an approximation technique. Some known results have been generalized and improved. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. A stochastic SIS epidemic infectious diseases model with double stochastic perturbations.
- Author
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Chen, Xingzhi, Tian, Baodan, Xu, Xin, Yang, Ruoxi, and Zhong, Shouming
- Subjects
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COMMUNICABLE diseases , *BASIC reproduction number , *STOCHASTIC models , *DISEASE outbreaks , *EPIDEMICS , *HOPFIELD networks , *ORNSTEIN-Uhlenbeck process - Abstract
In this paper, a stochastic SIS epidemic infectious diseases model with double stochastic perturbations is proposed. First, the existence and uniqueness of the positive global solution of the model are proved. Second, the controlling conditions for the extinction and persistence of the disease are obtained. Besides, the effects of the intensity of volatility ξ 1 and the speed of reversion 1 on the dynamical behaviors of the model are discussed. Finally, some numerical examples are given to support the theoretical results. The results show that if the basic reproduction number ℛ 0 s < 1 , the disease will be extinct, that is to say that we can control the threshold ℛ 0 s to suppress the disease outbreak. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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5. Dynamical behaviors of a stochastic SIRV epidemic model with the Ornstein–Uhlenbeck process.
- Author
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Shang, Jiaxin and Li, Wenhe
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ORNSTEIN-Uhlenbeck process , *PROBABILITY density function , *EPIDEMICS , *LOTKA-Volterra equations , *LYAPUNOV functions , *PREVENTIVE medicine - Abstract
Vaccination is an important tool in disease control to suppress disease, and vaccine-influenced diseases no longer conform to the general pattern of transmission. In this paper, by assuming that the infection rate is affected by the Ornstein–Uhlenbeck process, we obtained a stochastic SIRV model. First, we prove the existence and uniqueness of the global positive solution. Sufficient conditions for the extinction and persistence of the disease are then obtained. Next, by creating an appropriate Lyapunov function, the existence of the stationary distribution for the model is proved. Further, the explicit expression for the probability density function of the model around the quasi-equilibrium point is obtained. Finally, the analytical outcomes are examined by numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. Minimum Information Variability in Linear Langevin Systems via Model Predictive Control.
- Author
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Guel-Cortez, Adrian-Josue, Kim, Eun-jin, and Mehrez, Mohamed W.
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LINEAR systems , *PREDICTION models , *DISTRIBUTION (Probability theory) , *ORNSTEIN-Uhlenbeck process , *INFORMATION theory , *ENTROPY - Abstract
Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with insights from information geometry theory. Focusing on linear Langevin systems, we use model predictive control online optimisation capabilities to determine the system inputs that minimise deviations from the geodesic of the information length over time, ensuring dynamics with minimum "geometric information variability". We validate our methodology through numerical experimentation on the Ornstein–Uhlenbeck process and Kramers equation, demonstrating its feasibility. Furthermore, in the context of the Ornstein–Uhlenbeck process, we analyse the impact on the entropy production and entropy rate, providing a physical understanding of the effects of minimum information variability control. [ABSTRACT FROM AUTHOR]
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- 2024
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7. Typical motion-based modelling and tracking for vehicle targets in linear road segment.
- Author
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Hao, Xiaohui, Xia, Yuanqing, Yang, Hongjiu, and Zuo, Zhiqiang
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TRACKING radar , *LANE changing , *ORNSTEIN-Uhlenbeck process , *VEHICLE models , *ROADS - Abstract
In this paper, a typical motion-based modelling and tracking issue is investigated for vehicle targets in linear road segment by a variable structure multiple model (VSMM) method. Vehicle target motions in a road with multiple lanes are described by typical lane keeping and lane changing manoeuvres. To describe trajectories of typical manoeuvres, an Ornstein–Uhlenbeck process and a sine half-cycle are used to model lane keeping and lane changing motions in lateral direction, respectively. Note that starting point and length of lane changing motion are unknown in target tracking. Time-varying model sets are designed based on the current motion model with different motion parameters. A VSMM tracking frame is constructed to obtain target state estimates with time-varying model set. The effectiveness of the proposed typical motion-based tracking scheme is displayed by simulation results on road vehicle tracking. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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8. Analysis of the measurement uncertainty for a 3D wind-LiDAR.
- Author
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Knöller, Wolf, Bagheri, Gholamhossein, Olshausen, Philipp von, and Wilczek, Michael
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WIND measurement , *WEATHER , *ORNSTEIN-Uhlenbeck process , *WIND speed , *VELOCITY measurements , *ATMOSPHERIC turbulence - Abstract
High-resolution three-dimensional (3D) wind velocity measurements are of major importance for the characterization of atmospheric turbulence. The use of a multi-beam wind-LiDAR focusing on a measurement volume from different directions is a promising approach for obtaining such wind data. This paper provides a detailed study on the propagation of measurement uncertainty of a three-beam wind-LiDAR designed for mounting on airborne platforms with geometrical constraints that lead to increased measurement uncertainties of the wind components transverse to the main axis of the system. The uncertainty analysis is based on synthetic wind data generated by an Ornstein-Uhlenbeck process as well as on experimental wind data from airborne and ground-based 3D ultrasonic anemometers. For typical atmospheric conditions, we show that the measurement uncertainty of the transverse components can be reduced by about 30 %–50 % by applying an appropriate post-processing algorithm. Optimized post-processing parameters can be determined in an actual experiment by characterizing measured data in terms of variance and correlation time of wind fluctuations. These results allow an optimized design of a multi-beam wind-LiDAR with strong geometrical limitations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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9. Mobility, response and transport in non-equilibrium coarse-grained models.
- Author
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Jung, Gerhard
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ORNSTEIN-Uhlenbeck process , *LINEAR systems , *FLUCTUATION-dissipation relationships (Physics) , *LANGEVIN equations - Abstract
We investigate two different types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The first model is obtained by analytically 'integrating out' the oscillators and the second is based on a derivation using projection operator techniques. We observe that these two models behave very differently when the tagged particle is exposed to external harmonic potentials or pulling forces. Most importantly, we find that the analytic model has a well defined friction kernel and can be used to extract work, consistent with the microscopic system, while the projection model corresponds to an effective equilibrium model, which cannot be used to extract work. We apply the analysis to two popular non-equilibrium systems, time-delay feedback control and the active Ornstein–Uhlenbeck process. Finally, we highlight that our study could have important consequences for dynamic coarse-graining of non-equilibrium systems going far beyond the linear systems investigated in this manuscript. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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10. Effect of correlation time of combustion noise on early warning indicators of thermoacoustic instability.
- Author
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Vishnoi, Neha, Gupta, Vikrant, Saurabh, Aditya, and Kabiraj, Lipika
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COMBUSTION , *ORNSTEIN-Uhlenbeck process , *NOISE , *COMBUSTION chambers , *RESONANCE effect , *ACOUSTIC streaming , *ACOUSTIC emission - Abstract
In this paper, we analyze the effects of finite correlation time (noise color) of combustion noise on noise-induced coherence and early warning indicators (EWIs) via numerical and experimental studies. We consider the Rijke tube as a prototypical combustion system and model combustion noise as an additive Ornstein–Uhlenbeck process while varying noise intensity and correlation time. We numerically investigate corresponding effects on coherence resonance and multi-fractal properties of pressure fluctuations. Subsequently, we experimentally validate results and elucidate the influence of noise color and intensity on trends in coherence resonance and multi-fractal measures that can be expected in a practical scenario using an electroacoustic simulator. We find that the coherence factor, which quantifies the relative contribution of coherent oscillations in a noisy signal, increases as the system approaches the thermoacoustic instability—irrespective of the correlation time. It works at most levels of combustion noise (except for too low and too high noise levels). The Hurst exponent reduces as the system approaches thermoacoustic instability only when the correlation time is small. These results have implications on the prediction and monitoring of thermoacoustic instability in practical combustors. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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11. On the estimation of periodic signals in the diffusion process using a high-frequency scheme.
- Author
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Pramesti, Getut and Saptono, Ristu
- Subjects
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ENERGY consumption of lighting , *MONTE Carlo method , *SIGNAL processing , *ORNSTEIN-Uhlenbeck process , *ASYMPTOTIC normality , *AMPLITUDE estimation - Abstract
The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude. The periodicity of the frequency components is also thought to affect the convergence of these parameters. In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal. Under the high-frequency sampling setting, we provide the frequency components' consistency and asymptotic normality. It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl.29 (2023), 1, 1–32]. The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic. In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components. Further, the result of the study, that is, the convergence rate of the frequency is (n h) 3 , also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, J. Math. Comput. Sci.11 (2021), 5, 6433–6443], which mentioned (n h) 3 h . The proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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12. Managing Customer Churn via Service Mode Control.
- Author
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Kanoria, Yash, Lobel, Ilan, and Lu, Jiaqi
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CONSUMERS ,CUSTOMER lifetime value ,CUSTOMER satisfaction ,CUSTOMER retention ,MARKOV processes ,CUSTOMER loyalty programs ,SATISFACTION - Abstract
We introduce a novel stochastic control model for the problem of a service firm interacting over time with one of its customers who probabilistically churns depending on the customer's satisfaction. The firm has two service modes available, and they determine the drift and volatility of the Brownian reward process. The firm's objective is to maximize the rewards generated over the customer's lifetime. Meanwhile, the customer might churn probabilistically if the customer's satisfaction, modeled as an Orstein–Uhlenbeck process controlled by the firm's service mode, is below a certain threshold. We build upon Markov processes with spatial delay to solve this problem, and we explicitly characterize the firm's optimal policy, which is either myopic or a sandwich policy. A sandwich policy is one in which the firm deploys the service mode with inferior reward rate when the customer satisfaction level is in a specific interval near the satisfaction threshold and uses the myopically optimal service mode for all other satisfaction levels. Specifically, we find that the firm should use the safe service mode when the customer is marginally satisfied and the risky service mode when the customer is marginally unsatisfied. We find numerically that the customer lifetime value under the optimal policy is large relative to that under the myopic policy. Our results are robust to a variety of alternative model specifications. Funding: J. Lu gratefully acknowledges financial support from Natural Science Foundation of China (NSFC) [Project 72192805]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0179. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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13. Quickest Detection Problems for Ornstein–Uhlenbeck Processes.
- Author
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Glover, Kristoffer and Peskir, Goran
- Subjects
ORNSTEIN-Uhlenbeck process ,PARABOLIC differential equations ,BROWNIAN motion ,SIGNAL-to-noise ratio ,NONLINEAR integral equations - Abstract
Consider an Ornstein–Uhlenbeck process that initially reverts to zero at a known mean-reversion rate β
0 , and then after some random/unobservable time, this mean-reversion rate is changed to β1 . Assuming that the process is observed in real time, the problem is to detect when exactly this change occurs as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) independent from the process prior to the change of its mean-reversion rate. The solution is expressed in terms of a stopping time that minimises the probability of a false early detection and the expected delay of a missed late detection. Allowing for both positive and negative values of β0 and β1 (including zero), the problem and its solution embed many intuitive and practically interesting cases. For example, the detection of a mean-reverting process changing to a simple Brownian motion (β0>0 and β1=0) and vice versa (β0=0 and β1>0) finds a natural application to pairs trading in finance. The formulation also allows for the detection of a transient process becoming recurrent (β0<0 and β1≥0) as well as a recurrent process becoming transient (β0≥0 and β1<0). The resulting optimal stopping problem is inherently two-dimensional (because of a state-dependent signal-to-noise ratio), and various properties of its solution are established. In particular, we find the somewhat surprising fact that the optimal stopping boundary is an increasing function of the modulus of the observed process for all values of β0 and β1 . [ABSTRACT FROM AUTHOR]- Published
- 2024
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14. Dynamic analysis of generalized epidemic models with latent period, quarantine, governmental intervention and Ornstein–Uhlenbeck process.
- Author
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Su, Tan, Zhang, Xinhong, and Jiang, Daqing
- Abstract
Considering the transmission characteristics of COVID-19, we formulate a Susceptible-Exposed-Quarantine-Infected-Recovered epidemic model by five first-order differential equations to study the dynamical behaviors of diseases that have a latent period, quarantine strategy, governmental intervention and general incidence rate. After giving the basic reproduction number R 0 , conditions for the existence of equilibria and their local asymptotic stability are both investigated. However, environmental perturbations always have influence on the epidemic in the natural world. With the assumption that the transmission rate is driven by the log-normal Ornstein–Uhlenbeck process, we construct a corresponding stochastic epidemic model that incorporates environmental impacts. Based on the proof of existence and uniqueness of the global positive solution, two critical values R 0 e and R 0 s are established that can determine the extinction and persistence of disease, which are completely constituted by the basic reproduction number and random factors. By solving a changing four-dimensional Fokker–Planck equation, we calculate the exact analytical expression of the probability density function of stationary distribution near the quasi-endemic equilibrium. Finally, some numerical simulations are performed to support obtained theoretical results, and we show the sensitivity index to study the impact of each parameter on disease transmission. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows.
- Author
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Das, Rishita and Girimaji, Sharath S.
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TURBULENT flow ,INCOMPRESSIBLE flow ,TURBULENCE ,REYNOLDS number ,ORNSTEIN-Uhlenbeck process - Abstract
Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ($A = \sqrt {A_{ij}A_{ij}}$) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$. The boundedness and compactness of the $b_{ij}$ -space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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16. Continuous‐time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations.
- Author
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Wang, Ziheng and Sirignano, Justin
- Subjects
STOCHASTIC control theory ,PARTIAL differential equations ,ORNSTEIN-Uhlenbeck process ,POINT processes ,STOCHASTIC processes ,ONLINE algorithms ,CONJUGATE gradient methods - Abstract
We develop a new continuous‐time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an estimate for the gradient of the stationary distribution. The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically converging to the direction of steepest descent. We rigorously prove convergence of the online forward propagation algorithm for linear SDE models (i.e., the multidimensional Ornstein–Uhlenbeck process) and present its numerical results for nonlinear examples. The proof requires analysis of the fluctuations of the parameter evolution around the direction of steepest descent. Bounds on the fluctuations are challenging to obtain due to the online nature of the algorithm (e.g., the stationary distribution will continuously change as the parameters change). We prove bounds for the solutions of a new class of Poisson partial differential equations (PDEs), which are then used to analyze the parameter fluctuations in the algorithm. Our algorithm is applicable to a range of mathematical finance applications involving statistical calibration of SDE models and stochastic optimal control for long time horizons where ergodicity of the data and stochastic process is a suitable modeling framework. Numerical examples explore these potential applications, including learning a neural network control for high‐dimensional optimal control of SDEs and training stochastic point process models of limit order book events. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. American Options in Time-Dependent One-Factor Models: Semi-Analytic Pricing, Numerical Methods, and ML Support.
- Author
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Itkin, Andrey and Muravey, Dmitry
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MATHEMATICAL models of pricing ,NUMERICAL analysis ,VOLTERRA equations ,MACHINE learning ,ORNSTEIN-Uhlenbeck process - Abstract
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in Carr and Itkin (2021). It was shown that to obtain these prices one needs to numerically solve a nonlinear Volterra integral equation of the second kind to find the exercise boundary, which is a function of the time only. Once this is done, the option prices follow. It was also shown that computationally this method is as efficient as the forward finite difference solver, while also providing better accuracy and stability. Later this approach, called "the generalized integral transform" method, was significantly extended to various time-dependent one factor (Itkin et al. 2021) and stochastic volatility (Carr et al. 2022, Itkin and Muravey 2022b) models as applied to pricing barrier options. For American options, though, despite being possible, this was not explicitly reported anywhere. In this article our goal is to fill this gap and also discuss which numerical method can be efficient to solve the corresponding Volterra equations, also including machine learning. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
18. A stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps
- Author
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Meng Gao and Xiaohui Ai
- Subjects
stochastic gilpin-ayala mutualism model ,moment boundedness of solution ,extinction ,ornstein-uhlenbeck process ,the existence of stationary distribution ,Biotechnology ,TP248.13-248.65 ,Mathematics ,QA1-939 - Abstract
By using the Ornstein-Uhlenbeck (OU) process to simulate random disturbances in the environment, and considering the influence of jump noise, a stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps was established, and the asymptotic behaviors of the stochastic Gilpin-Ayala mutualism model were studied. First, the existence of the global solution of the stochastic Gilpin-Ayala mutualism model is proved by the appropriate Lyapunov function. Second, the moment boundedness of the solution of the stochastic Gilpin-Ayala mutualism model is discussed. Third, the existence of the stationary distribution of the solution of the stochastic Gilpin-Ayala mutualism model is obtained. Finally, the extinction of the stochastic Gilpin-Ayala mutualism model is proved. The theoretical results were verified by numerical simulations.
- Published
- 2024
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19. Gamma mixed fractional Lévy Ornstein–Uhlenbeck process
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Héctor Araya, Johanna Garzón, and Rolando Rubilar-Torrealba
- Subjects
Fractional Lévy process ,Ornstein–Uhlenbeck process ,non-Gaussian process ,random coefficients ,Applied mathematics. Quantitative methods ,T57-57.97 ,Mathematics ,QA1-939 - Abstract
In this article, a non-Gaussian long memory process is constructed by the aggregation of independent copies of a fractional Lévy Ornstein–Uhlenbeck process with random coefficients. Several properties and a limit theorem are studied for this new process. Finally, some simulations of the limit process are shown.
- Published
- 2023
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20. Effects of real random perturbations on Monod and Haldane consumption functions in the chemostat model.
- Author
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Caraballo, Tomás, López-de-la-Cruz, Javier, and Caraballo-Romero, Verónica
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CHEMOSTAT , *BIOLOGICAL extinction , *ORNSTEIN-Uhlenbeck process , *COMPUTER simulation - Abstract
In this paper, we investigate the classical chemostat model where the consumption function of the species, in both cases Monod and Haldane, is perturbed by real random fluctuations. Once the existence and uniqueness of non-negative global solution of the corresponding random systems is ensured, we prove the existence of a deterministic compact attracting set, whence we are able to find conditions to guarantee either the extinction or the persistence of the species, the most important aim in real applications. In addition, we depict several numerical simulations to illustrate the theoretical framework, standing out our contributions, providing the biological interpretation of every result and comparing with similar works in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Stochastic virus infection model with Ornstein–Uhlenbeck perturbation: Extinction and stationary distribution analysis.
- Author
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Cao, Zhongwei, Guo, Chenguang, Shi, Zhenfeng, Song, Zhifei, and Zu, Li
- Subjects
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VIRUS diseases , *ORNSTEIN-Uhlenbeck process , *INVARIANT sets , *LYAPUNOV functions , *STOCHASTIC models - Abstract
In this paper, we propose a stochastic virus infection model with nonlytic immune response, where the transmission rate is realistically modeled as being subject to continuous fluctuations, represented by the Ornstein–Uhlenbeck process. Firstly, we establish the existence and uniqueness of the global solution for the stochastic model and its invariant set, ensuring the robustness and applicability of model. Next, by constructing appropriate Lyapunov functions, we derive sufficient conditions for virus extinction and the existence of a stationary distribution for the stochastic model. These conditions elucidate the key dynamic behaviors, such as extinction and persistence, within the stochastic framework. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. A pseudo-likelihood estimator of the Ornstein–Uhlenbeck parameters from suprema observations.
- Author
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Blanchet-Scalliet, Christophette, Dorobantu, Diana, and Nieto, Benoit
- Abstract
In this paper, we propose an estimator for the Ornstein–Uhlenbeck parameters based on observations of its supremum. We derive an analytic expression for the supremum density. Making use of the pseudo-likelihood method based on the supremum density, our estimator is constructed as the maximal argument of this function. Using weak-dependency results, we prove some statistical properties on the estimator such as consistency and asymptotic normality. Finally, we apply our estimator to simulated and real data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Dynamic property of a stochastic cooperative species system with distributed delays and Ornstein–Uhlenbeck process.
- Author
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Zhou, Yaxin and Jiang, Daqing
- Subjects
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ORNSTEIN-Uhlenbeck process , *LOTKA-Volterra equations , *STOCHASTIC systems , *LYAPUNOV functions , *SPECIES , *COMPUTER simulation - Abstract
Scanning the whole writing, we discuss a stochastic cooperative species system with distributed delays under the influences of Ornstein–Uhlenbeck process of mean regression. We successfully obtain the existence and uniqueness of positive solutions for stochastic system at first. Secondly, by studying the Lyapunov function, we present the existence of the stationary distribution of the system. We are relatively familiar with the understanding of the density function of random systems. This paper also gives the expression of the density function of the random system near the unique positive equilibrium. In addition, the asymptotic properties of the p-moment boundedness and solution of the stochastic population system are also studied. In particular, we use numerical simulation to verify the theoretical results in the last section. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. The stationary distribution and density function of a stochastic SIRB cholera model with Ornstein–Uhlenbeck process.
- Author
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Wen, Buyu and Liu, Qun
- Subjects
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ORNSTEIN-Uhlenbeck process , *PROBABILITY density function , *CHOLERA , *STOCHASTIC processes , *COMMUNICABLE diseases , *LYAPUNOV functions - Abstract
Cholera is a global epidemic infectious disease that seriously endangers human life. It is disturbed by random factors in the process of transmission. Therefore, in this paper, a class of stochastic SIRB cholera model with Ornstein–Uhlenbeck process is established. On the basis of verifying that the model exists a unique global solution to any initial value, a sufficient criterion for the existence of a stationary distribution of the positive solution of the random model is established by constructing an appropriate random Lyapunov function. Furthermore, under the same condition that there is a stationary distribution, the specific expression of the probability density function of the random model around the positive equilibrium point is calculated. Finally, the theoretical results are verified by numerical model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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25. The El Niño Southern Oscillation Recharge Oscillator with the Stochastic Forcing of Long-Term Memory.
- Author
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Li, Xiaofeng and Li, Yaokun
- Subjects
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LONG-term memory , *HARMONIC oscillators , *SOUTHERN oscillation , *STOCHASTIC processes , *ORNSTEIN-Uhlenbeck process ,EL Nino - Abstract
The influence of the fast-varying variables that have a long-term memory on the El Niño Southern Oscillation (ENSO) is investigated by adding a fractional Ornstein–Uhlenbeck (FOU) process stochastic noise on the simple recharge oscillator (RO) model. The FOU process noise converges to zero very slowly with a negative power law. The corresponding non-zero ensemble mean during the integration period can exert a pronounced influence on the ensemble-mean dynamics of the RO model. The state-dependent noise, also called the multiplicative noise, can present its influence by reducing the relaxation coefficient and by introducing periodic external forcing. The decreasing relaxation coefficient can enhance the oscillation amplitude and shorten the oscillation period. The forced frequency is close to the natural frequency. The two mechanisms together can further amplify the amplitude and shorten the period, compared with the state-independent noise or additive noise, which only exhibits its influence by introducing non-periodic external forcing. These two mechanisms explicitly elucidate the influence of the stochastic forcing on the ensemble-mean dynamics of the RO model. It provides comprehensive knowledge to better understand the interaction between the fast-varying stochastic forcing and the slow-varying deterministic system and deserves further investigation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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26. Maximum approximate likelihood estimation of general continuous-time state-space models.
- Author
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Mews, Sina, Langrock, Roland, Ötting, Marius, Yaqine, Houda, and Reinecke, Jost
- Subjects
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MAXIMUM likelihood statistics , *HIDDEN Markov models , *INFERENTIAL statistics , *JUVENILE offenders , *NUMERICAL integration , *CONTINUOUS time systems , *KALMAN filtering - Abstract
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. A stochastic predator–prey model with distributed delay and Ornstein–Uhlenbeck process: Characterization of stationary distribution, extinction, and probability density function.
- Author
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Zhang, Xinhong, Yang, Qing, and Jiang, Daqing
- Subjects
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PROBABILITY density function , *ORNSTEIN-Uhlenbeck process , *PREDATION , *STATIONARY processes , *STOCHASTIC models , *BRANCHING processes , *STOCHASTIC systems - Abstract
As the evolution of species relies on not only the current state but also the past information, it is more reasonable and realistic to take delay into an ecological model. This paper deals with a stochastic predator–prey model that considers the distribution delay and assume that the intrinsic growth rate and the death rate in the model are governed by Ornstein–Uhlenbeck process to simulate the random factors in the environment. Based on the existence and uniqueness of the global solution to the model and the boundedness of the p$$ p $$ order moments of the solution, several conditions are established to analyze the survival of the species. Specifically, a criteria for the existence of the stationary distribution to the stochastic system is established by constructing some suitable Lyapunov functions. And the analytical expression of the probability density function of the model around the quasi‐equilibrium is obtained. Furthermore, the extinction of species in the model is also explored. Finally, numerical simulations are carried out to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Existence and Internal Structure of the Deterministic Attracting Set for a Random Ant Colonies Model.
- Author
-
Wang, Hongcui and Xu, Chaoqun
- Subjects
- *
ANT colonies , *RANDOM sets , *ANTS , *ORNSTEIN-Uhlenbeck process , *ANT behavior , *TANGENT function - Abstract
This paper is concerned with the attracting set of an ant colonies model with bounded noisy perturbation. This perturbation is modeled by the well-known Ornstein–Uhlenbeck process and the arc tangent function. For the random model, we first verify the existence and uniqueness of the global positive solution, and then prove the existence of the deterministic attracting set. Furthermore, in order to reveal more detailed information about the long-time behavior of the ant colonies system, we analyze the internal structure of the attracting set and provide some conditions under which coexistence (or extinction) of the ant species exists in the ant colonies system. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process.
- Author
-
Liu, Qun and Jiang, Daqing
- Abstract
In this paper, assuming the certain variable satisfies the Ornstein–Uhlenbeck process, we formulate a stochastic within-host dengue model with immune response to obtain further understanding of the transmission dynamics of dengue fever. Then we analyze the dynamical properties of the stochastic system in detail, including the existence and uniqueness of the global solution, the existence of a stationary distribution, and the extinction of infected monocytes and free viruses. In particular, it is worth revealing that we get the specific form of covariance matrix in its probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. A scaling limit of the parabolic Anderson model with exclusion interaction.
- Author
-
Erhard, Dirk and Hairer, Martin
- Subjects
- *
ANDERSON model , *RANDOM walks , *ORNSTEIN-Uhlenbeck process , *CUMULANTS , *ORDER picking systems , *STRUCTURAL analysis (Engineering) , *PARABOLIC operators - Abstract
We consider the (discrete) parabolic Anderson model ∂u(t,x)/∂t=Δu(t,x)+ξt(x)u(t,x)$\partial u(t,x)/\partial t=\Delta u(t,x) +\xi _t(x) u(t,x)$, t≥0$t\ge 0$, x∈Zd$x\in \mathbb {Z}^d$, where the ξ‐field is R$\mathbb {R}$‐valued and plays the role of a dynamic random environment, and Δ is the discrete Laplacian. We focus on the case in which ξ is given by a properly rescaled symmetric simple exclusion process under which it converges to an Ornstein–Uhlenbeck process. Scaling the Laplacian diffusively and restricting ourselves to a torus, we show that in dimension d=3$d=3$ upon considering a suitably renormalised version of the above equation, the sequence of solutions converges in law. As a by‐product of our main result we obtain precise asymptotics for the survival probability of a simple random walk that is killed at a scale dependent rate when meeting an exclusion particle. Our proof relies on the discrete theory of regularity structures of Erhard and Hairer and on novel sharp estimates of joint cumulants of arbitrary large order for the exclusion process. We think that the latter is of independent interest and may find applications elsewhere. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. Dynamical behavior of a stochastic COVID-19 model with two Ornstein–Uhlenbeck processes and saturated incidence rates.
- Author
-
Li, Xiaoyu and Li, Zhiming
- Abstract
According to the transmission characteristics of COVID-19, this paper proposes a stochastic SAIRS epidemic model with two mean reversion Ornstein–Uhlenbeck processes and saturated incidence rates. We first prove the existence and uniqueness of the global solution in the stochastic model. Using several suitable Lyapunov methods, we then derive the extinction and persistence of COVID-19 under certain conditions. Further, stationary distribution and ergodic properties are obtained. Moreover, we obtain the probability density function of the stochastic model around the equilibrium. Numerical simulations illustrate our theoretical results and the effect of essential parameters. Finally, we apply the model to investigate the latest outbreak of the COVID-19 epidemic in Guangzhou city, China. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Numerical solutions of an option pricing rainfall weather derivatives model.
- Author
-
Nhangumbe, Clarinda and Sousa, Ercília
- Subjects
- *
DERIVATIVE securities , *PARTIAL differential equations , *PRICES , *ORNSTEIN-Uhlenbeck process , *WEATHER , *RAINFALL - Abstract
Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. In this work, we derive a rainfall weather derivative price model, based in the assumption that the rainfall dynamics follows a Ornstein-Uhlenbeck process. To calculate the price of the option we arrive at a two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and the total rainfall. Appropriate boundary conditions are suggested and they differ from the boundaries presented in literature in similar contexts. To compute the approximate solutions of the partial differential equation, we propose an explicit numerical method in order to deal efficiently with the different choices of the coefficients involved in the equation, that depend on the rainfall defice (or excess) and on the precipitation (amount of rain). Being an explicit numerical method, it will be conditionally stable and we discuss the stability region of the numerical method and its order of convergence. In the end we examine two test cases where the parameters of the model presented are estimated based on precipitation data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. G‐optimal grid designs for kriging models.
- Author
-
Dasgupta, Subhadra, Mukhopadhyay, Siuli, and Keith, Jonathan
- Abstract
This work is focused on finding G‐optimal designs theoretically for kriging models with two‐dimensional inputs and separable exponential covariance structures. For design comparison, the notion of evenness of two‐dimensional grid designs is developed. The mathematical relationship between the design and the supremum of the mean squared prediction error (SMSPE) function is studied and then optimal designs are explored for both prospective and retrospective design scenarios. In the case of prospective designs, the new design is developed before the experiment is conducted and the regularly spaced grid is shown to be the G‐optimal design. Retrospective designs are constructed by adding or deleting points from an already existing design. Deterministic algorithms are developed to find the best possible retrospective designs (which minimizes the SMSPE). It is found that a more evenly spread design under the G‐optimality criterion leads to the best possible retrospective design. For all the cases of finding the optimal prospective designs and the best possible retrospective designs, both frequentist and Bayesian frameworks have been considered. The proposed methodology for finding retrospective designs is illustrated with a spatiotemporal river water quality monitoring experiment. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Approximations of Lévy processes by integrated fast oscillating Ornstein–Uhlenbeck processes.
- Author
-
Feng, Lingyu, Gao, Ting, Li, Ting, Lin, Zhongjie, and Liu, Xianming
- Subjects
- *
LEVY processes , *ORNSTEIN-Uhlenbeck process , *CONTINUOUS processing , *TOPOLOGY - Abstract
In this paper, we study a smooth approximation of an arbitrary càdlàg Lévy process. Such approximation processes are known as integrated fast oscillating Ornstein–Uhlenbeck (OU) processes. We know that approximating processes are continuous, while the limit of processes may be discontinuous, so convergence in uniform topology or Skorokhod J 1 -topology will not hold in general. Therefore, we establish an approximation in Skorokhod M 1 -topology. Note that the convergence is almost surely, which is an extension result of Hintze and Pavlyukevich. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. A stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process.
- Author
-
Liu, Qun
- Subjects
- *
ORNSTEIN-Uhlenbeck process , *STOCHASTIC models , *STOCHASTIC systems , *DENSITY matrices , *POPULATION dynamics - Abstract
In this paper, a stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process is formulated and analysed, which is used to obtain a better understanding of the population dynamics. At first, we validate that the stochastic system has a unique global solution with any initial value. Then we analyse the stochastic dynamics of the model in detail, including pth moment boundedness, asymptotic pathwise estimation in turn. After that, we obtain sufficient conditions for the existence of a stationary distribution of the system by adopting stochastic Lyapunov function methods. In addition, under some mild conditions, we derive the specific form of covariance matrix in the probability density near the quasi-positive equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Modified trajectory fitting estimators for multi‐regime threshold Ornstein–Uhlenbeck processes.
- Author
-
Han, Yuecai and Zhang, Dingwen
- Subjects
- *
ORNSTEIN-Uhlenbeck process , *ASYMPTOTIC normality , *STOCHASTIC processes , *PARAMETER estimation - Abstract
The threshold Ornstein–Uhlenbeck process is a stochastic process governed by m Ornstein–Uhlenbeck subprocesses with the ith playing a role whenever the underlying process is in the ith regime. In this paper, we investigate the parameter estimation for threshold Ornstein–Uhlenbeck processes with multiple thresholds. The classical trajectory fitting method does not apply in this context due to the significantly complex calculations. Hence, a modified trajectory fitting method is used to obtain the explicit formula of the estimators for the drift parameters based on continuous observations. The strong consistency and asymptotic normality are proven. Simulation studies illustrate the asymptotic behaviour of the trajectory fitting estimators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. Gamma mixed fractional Lévy Ornstein-Uhlenbeck process.
- Author
-
Araya, Héctor, Garzón, Johanna, and Rubilar-Torrealba, Rolando
- Subjects
ORNSTEIN-Uhlenbeck process ,LEVY processes ,STOCHASTIC processes ,WIENER processes ,LIMIT theorems - Abstract
In this article, a non-Gaussian long memory process is constructed by the aggregation of independent copies of a fractional Lévy Ornstein-Uhlenbeck process with random coefficients. Several properties and a limit theorem are studied for this new process. Finally, some simulations of the limit process are shown. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. PAIRS TRADING WITH TOPOLOGICAL DATA ANALYSIS.
- Author
-
MAJUMDAR, SOURAV and LAHA, ARNAB KUMAR
- Subjects
DATA analysis ,ORNSTEIN-Uhlenbeck process ,BROWNIAN motion ,STOCHASTIC processes ,STATISTICAL correlation - Abstract
In this paper, we propose a pairs trading strategy using the theory of topological data analysis (TDA). The proposed strategy is model-free. We propose a TDA-based distance to measure dependence between a pair of stochastic processes. We derive an upper bound of this distance in terms of a function of the canonical correlation of the processes, which allows for interpretability of this distance. We also study Karhunen–Loève expansions of certain processes to qualitatively explore their shape properties. We check the performance of the strategy on simulated data from correlated geometric Brownian motion, correlated Ornstein–Uhlenbeck process and DCC-GARCH. We also examine the profitability of the proposed strategy on high-frequency data from the National Stock Exchange of India in 2018. We compare the method to a Euclidean distance-based method for pairs trading. We propose a pairs trading strategy evaluation framework using a Bayesian model for comparing gains from these two strategies. We find that the proposed approach based on TDA is more profitable and trades more frequently than the Euclidean distance-based strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. The First-Passage Area of Wiener Process withStochastic Resetting.
- Author
-
Abundo, Mario
- Abstract
For a one-dimensional Wiener process with stochastic resetting X (t) , obtained from an underlying Wiener process X(t), we study the statistical properties of its first-passage time through zero, when starting from X > 0 , and its first-passage area, that is the random area enclosed between the time axis and the path of the process X (t) up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
40. Intraday high-frequency pairs trading strategies for energy futures: evidence from China.
- Author
-
Luo, Jing, Lin, YuCheng, and Wang, Sijia
- Subjects
ENERGY futures ,SHARPE ratio ,FUTURES market ,ORNSTEIN-Uhlenbeck process - Abstract
We investigate the performance of pairs trading strategies based on Ornstein-Uhlenbeck (OU) process with jump-diffusion and regime-switching using minute-level data for five Chinese energy futures from 2 January 2020 to 30 November 2021 and compare them with traditional pairs trading strategies. Our results indicate that OU models can obtain an average return of 50.62% per annum and a Sharpe ratio of 2.63, which significantly exceed those of traditional pairs trading strategies. However, none of them could 'win' in every subperiod with diverse market conditions. Meanwhile, we find that introducing jump-diffusion indeed improves the performance (additional 25.37% annualized return and 1.12 Sharpe ratio). In contrast, considering more regimes does not always bring additional benefits. Robustness checks show that the superior performance of three-regime switching OU model (3RS-OUM) persists even under harsh trading conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. ON A CONSISTENT ESTIMATOR OF A USEFUL SIGNAL IN ORNSTEIN-UHLENBECK STOCHASTIC MODEL IN C[-l, l[.
- Author
-
KVATADZE, ZURAB and LABADZE, LEVAN
- Subjects
STOCHASTIC models ,ORNSTEIN-Uhlenbeck process ,STOCHASTIC differential equations ,WIENER processes ,BANACH spaces - Abstract
~It is considered a transmittion process of a useful signal in Ornstein-Uhlenbeck model in C[-l,l[ defined by the stochastic differential equation dΨ(t,x,ω)=∑n=02mAn∂n∂xnΨ(t,x,ω)dt+σdW(t,ω) with initial condition Ψ(0,x,ω)=Ψ0(x)∈FD(0)[-l,l[, where m≥1, (An)0≤n≤2m∈R+×R2m-1, ((t,x,ω)∈[0,+∞[×[-l,l[×Ω), σ∈R+, C[-l,l[ is Banach space of all real-valued bounded continuous functions on [-l,l[, FD(0)[-l,l[⊂C[-l,l[ is class of all real-valued bounded continuous functions on [-l,l[ whose Fourier series converges to himself everywhere on [-l,l[, (W(t,ω))t≥0 is a Wiener process and Ψ0(x) is a useful signal. By use a sequence of transformed signals (Zk)k∈N=(Ψ(t0,x,ωk))k∈N at moment t0>0, consistent and infinite-sample consistent estimations of the useful signal Ψ0 is constructed under assumption that parameters (An)0≤n≤2m and σ are known. Animation and simulation of the Ornstein-Uhlenbeck process in C[-l,l[ and an estimation of a useful signal are also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2023
42. A stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process
- Author
-
Qun Liu
- Subjects
Three-species predator–prey model ,competition between preys ,ornstein–Uhlenbeck process ,moment boundedness ,stationary distribution ,density function ,Environmental sciences ,GE1-350 ,Biology (General) ,QH301-705.5 - Abstract
In this paper, a stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process is formulated and analysed, which is used to obtain a better understanding of the population dynamics. At first, we validate that the stochastic system has a unique global solution with any initial value. Then we analyse the stochastic dynamics of the model in detail, including pth moment boundedness, asymptotic pathwise estimation in turn. After that, we obtain sufficient conditions for the existence of a stationary distribution of the system by adopting stochastic Lyapunov function methods. In addition, under some mild conditions, we derive the specific form of covariance matrix in the probability density near the quasi-positive equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings.
- Published
- 2023
- Full Text
- View/download PDF
43. Dynamic properties for a stochastic SEIR model with Ornstein–Uhlenbeck process.
- Author
-
Lu, Chun and Xu, Chuanlong
- Subjects
- *
ORNSTEIN-Uhlenbeck process , *STOCHASTIC models , *PROBABILITY density function , *BASIC reproduction number , *FOKKER-Planck equation - Abstract
In this article, we are committed to the study of dynamic properties for a stochastic SEIR epidemic model with infectivity in latency and home quarantine about the susceptible and Ornstein–Uhlenbeck process. Firstly, we provide a criterion for the presence of an ergodic stationary distribution of the model. Secondly, by extracting the corresponding Fokker–Planck equation, we derive the probability density function around quasi-endemic equilibrium of the stochastic model. Thirdly, we establish adequate criteria for extinction. Finally, by using the epidemic data of corresponding deterministic model, two numerical tests are presented to illustrate the effectiveness of the theoretical results. • A stochastic SEIR model with Ornstein-Uhlenbeck process is investigated. • Sufficient criteria for the existence of an ergodic stationary distribution are derived. • The probability density function of the stochastic model is obtained. • The criterion for extinction is closely related to the basic reproduction number. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis
- Author
-
Mu, Xiaojie and Jiang, Daqing
- Published
- 2024
- Full Text
- View/download PDF
45. Simulation-based assessment of the performance of hierarchical abundance estimators for camera trap surveys of unmarked species.
- Author
-
Martijn, Bollen, Jim, Casaer, Natalie, Beenaerts, and Thomas, Neyens
- Subjects
- *
ORNSTEIN-Uhlenbeck process , *CAMERAS , *SPECIES , *HUMAN facial recognition software - Abstract
Knowledge on animal abundances is essential in ecology, but is complicated by low detectability of many species. This has led to a widespread use of hierarchical models (HMs) for species abundance, which are also commonly applied in the context of nature areas studied by camera traps (CTs). However, the best choice among these models is unclear, particularly based on how they perform in the face of complicating features of realistic populations, including: movements relative to sites, multiple detections of unmarked individuals within a single survey, and low detectability. We conducted a simulation-based comparison of three HMs (Royle-Nichols, binomial N-mixture and Poisson N-mixture model) by generating groups of unmarked individuals moving according to a bivariate Ornstein–Uhlenbeck process, monitored by CTs. Under a range of simulated scenarios, none of the HMs consistently yielded accurate abundances. Yet, the Poisson N-mixture model performed well when animals did move across sites, despite accidental double counting of individuals. Absolute abundances were better captured by Royle-Nichols and Poisson N-mixture models, while a binomial N-mixture model better estimated the actual number of individuals that used a site. The best performance of all HMs was observed when estimating relative trends in abundance, which were captured with similar accuracy across these models. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths.
- Author
-
Szabłowski, Paweł J.
- Abstract
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification are important because they are relatively easy to simulate. One does not have to care about the distribution of their jumps which is always difficult to find. Among those processes with the continuous path are the Ornstein–Uhlenbeck process, the Gamma process, the process with Arcsin or Wigner margins and the Theta functions as the transition densities and others. We give a simple criterion for the stationary process to have a continuous path modification expressed in terms of skewness and excess kurtosis of the marginal distribution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Derivation of Anomalous Behavior from Interacting Oscillators in the High-Temperature Regime.
- Author
-
Gonçalves, Patrícia and Hayashi, Kohei
- Subjects
- *
BURGERS' equation , *CONSERVED quantity , *ORNSTEIN-Uhlenbeck process , *LEVY processes , *TAYLOR'S series , *HEAT equation , *CONSERVATION laws (Mathematics) - Abstract
A microscopic model of interacting oscillators, which admits two conserved quantities, volume, and energy, is investigated. We begin with a system driven by a general nonlinear potential under high-temperature regime by taking the inverse temperature of the system asymptotically small. As a consequence, one can extract a principal part (by a simple Taylor expansion argument), which is driven by the harmonic potential, and we show that previous results for the harmonic chain are covered with generality. We consider two fluctuation fields, which are defined as a linear combination of the fluctuation fields of the two conserved quantities, volume, and energy, and we show that the fluctuations of one field converge to a solution of an additive stochastic heat equation, which corresponds to the Ornstein–Uhlenbeck process, in a weak asymmetric regime, or to a solution of the stochastic Burgers equation, in a stronger asymmetric regime. On the other hand, the fluctuations of the other field cross from an additive stochastic heat equation to a fractional diffusion equation given by a skewed Lévy process. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Persistence and extinction of a modified LG-Holling type II predator-prey model with two competitive predators and Lévy jumps.
- Author
-
Gao, Yongxin and Yang, Fan
- Subjects
- *
LOTKA-Volterra equations , *PREDATION , *ORNSTEIN-Uhlenbeck process , *MATHEMATICAL analysis , *PREDATORY animals , *POSITIVE systems , *COMPUTER simulation - Abstract
In this paper, we study a three-species predator-prey model with modified LG-Holling type II with Lévy jumps, and we take the competition among predators into consideration. First, We use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system by mathematical analysis skills such as comparison theorem. Futhermore, the extinction or persistence in the mean of each species under different conditions is obtained. Finally, some numerical simulations are carried out to support our main results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Scaling limit of stretched Brownian chains.
- Author
-
Aurzada, Frank, Betz, Volker, and Lifshits, Mikhail
- Subjects
- *
STOCHASTIC processes , *ORNSTEIN-Uhlenbeck process , *CONTINUOUS functions , *GAUSSIAN processes - Abstract
We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting.
- Author
-
Dubey, Ashutosh and Pal, Arnab
- Subjects
- *
ORNSTEIN-Uhlenbeck process , *STOCHASTIC processes - Abstract
We study the statistical properties of first-passage Brownian functionals (FPBFs) of an Ornstein–Uhlenbeck process in the presence of stochastic resetting. We consider a one dimensional set-up where the diffusing particle sets off from x 0 and resets to x R at a certain rate r. The particle diffuses in a harmonic potential (with strength k) which is centered around the origin. The center also serves as an absorbing boundary for the particle and we denote the first passage time (FPT) of the particle to the center as t f . In this set-up, we investigate the following functionals: (i) local time T l o c = ∫ 0 t f d τ δ (x − x R) i.e. the time a particle spends around x R until the first passage, (ii) occupation or residence time T r e s = ∫ 0 t f d τ θ (x − x R) i.e. the time a particle typically spends above x R until the first passage and (iii) the FPT t f to the origin. We employ the Feynman–Kac formalism for renewal process to derive the analytical expression for the first moment of all the three FPBFs mentioned above. In particular, we find that resetting can either prolong or shorten the mean residence and FPT depending on the system parameters. The transition between these two behaviors or phases can be characterized precisely in terms of optimal resetting rates, which interestingly undergo a continuous transition as we vary the trap stiffness k. We characterize this transition and identify the critical-parameter and -coefficient for both the cases. We also showcase other interesting interplay between the resetting rate and potential strength on the statistics of these observables. Our analytical results are in excellent agreement with the numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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