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Several types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N − 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions. [ABSTRACT FROM AUTHOR]

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields. [ABSTRACT FROM AUTHOR]

Exact methods for the exponentiation of matrices of dimension N can be computationally expensive in terms of execution time (N3) and memory requirements (N2), not to mention numerical precision issues. A matrix often exponentiated in the natural sciences is the rate matrix. Here, we explore five methods to exponentiate rate matrices, some of which apply more broadly to other matrix types. Three of the methods leverage a mathematical analogy between computing matrix elements of a matrix exponential process and computing transition probabilities of a dynamical process (technically a Markov jump process, MJP, typically simulated using Gillespie). In doing so, we identify a novel MJP-based method relying on restricting the number of "trajectory" jumps that incurs improved computational scaling. We then discuss this method's downstream implications on mixing properties of Monte Carlo posterior samplers. We also benchmark two other methods of matrix exponentiation valid for any matrix (beyond rate matrices and, more generally, positive definite matrices) related to solving differential equations: Runge–Kutta integrators and Krylov subspace methods. Under conditions where both the largest matrix element and the number of non-vanishing elements scale linearly with N—reasonable conditions for rate matrices often exponentiated—computational time scaling with the most competitive methods (Krylov and one of the MJP-based methods) reduces to N2 with total memory requirements of N. [ABSTRACT FROM AUTHOR]

Muscle contraction at the macrolevel is a physiological process that is ultimately due to the interaction between myosin and actin proteins at the microlevel. The actin–myosin interaction involves slow attachment and detachment responses and a rapid temporal change in protein conformation called power-stroke. Jump-diffusion models that combine jump processes between attachment and detachment with a mechanical description of the power-stroke have been proposed in the literature. However, the current formulations of these models are not fully compatible with the principles of thermodynamics. To solve the problem of coupling continuous mechanisms with discrete chemical transitions, we rely on the mathematical formalism of Poisson random measures. First, we design an efficient stochastic formulation for existing muscle contraction partial differential equation models. Then, we write a new jump-diffusion model for actin–myosin interaction. This new model describes both the behavior of muscle contraction on multiple time scales and its compatibility with thermodynamic principles. Finally, following a classical calibration procedure, we demonstrate the ability of the model to reproduce experimental data characterizing muscle behavior on fast and slow time scales. [ABSTRACT FROM AUTHOR]

Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided for the SVIS (Susceptible-Vaccinated-Infected-Susceptible) disease epidemic model to investigate the impacts of hazard rate functions (HRFs) on disease control. The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. Key statistical properties and the basic reproduction number () are derived, and conditions for the system's asymptotic autonomy are established for specific lifetime distributions. Four HRF behaviors—monotonic, bathtub, reverse bathtub, and constant—are analyzed to determine conditions for disease eradication and the asymptotic population under these scenarios. Sensitivity analysis examines how HRF behaviors shape system trajectories. Numerical simulations illustrate the influence of diverse lifetime models on vaccine efficacy and immunity, offering insights for effective disease management. [ABSTRACT FROM AUTHOR]

We mainly focus on the willow algorithm which can be used to solve the optimal dynamic multi-cycle investment and consumption problem under the jump-diffusion stochastic volatility model. First we obtain the moment generating function of the risky asset and then coalescing the Johnson-Curve transformation theory to generate the willow algorithm, which solving the multi-cycle dynamic investment and consumption problem is designed based on the two-dimensional willow framework. Moreover, through comparing our proposed solution with the optimal investment and consumption display solutions under the geometric Brownian motion model, we further discuss the analysis of the willow algorithm sensitivity. The willow algorithm for optimal investment and consumption proposed in this paper is able to extend the willow method which is effective from the field of option pricing to the field of investment portfolio, and it also provides a new idea for numerically solving the multi-period optimal investment and consumption decision. [ABSTRACT FROM AUTHOR]

This article explores dynamic factor allocation by analyzing the cyclical performance of factors through regime analysis. The authors focus on a US equity investment universe comprising seven long-only indices representing the market and six style factors: value, size, momentum, quality, low volatility, and growth. Their approach integrates factor-specific regime inferences of each factor index's active performance relative to the market into the Black–Litterman model to construct a fully invested, long-only multifactor portfolio. First, the authors apply the sparse jump model (SJM) to identify bull and bear market regimes for individual factors, using a feature set based on risk and return measures from historical factor active returns, as well as variables reflecting the broader market environment. The regimes identified by the SJM exhibit enhanced stability and interpretability compared with traditional methods. A hypothetical single-factor long–short strategy is then used to assess these regime inferences and fine-tune hyperparameters, resulting in a positive Sharpe ratio of this strategy across all factors with low correlation among them. These regime inferences are then incorporated into the Black–Litterman framework to dynamically adjust allocations among the seven indices, with an equally weighted (EW) portfolio serving as the benchmark. Empirical results show that the constructed multifactor portfolio significantly improves the information ratio (IR) relative to the market, raising it from just 0.05 for the EW benchmark to approximately 0.4. When measured relative to the EW benchmark itself, the dynamic allocation achieves an IR of around 0.4 to 0.5. The strategy also enhances absolute portfolio performance across key metrics such as the Sharpe ratio and maximum drawdown. These findings highlight the effectiveness of leveraging regime-switching signals to enhance factor allocation by capitalizing on factor cyclicality. [ABSTRACT FROM AUTHOR]

This paper studies the pricing of vulnerable options with systematic and idiosyncratic factors incorporated. Variance gamma processes are employed to model price jumps caused by the arrivals of systematic and idiosyncratic relevant information. A parsimonious pricing measure is developed and Laplace transforms of option price and Greek letters are given. Numerical results are obtained by a two‐sided Euler inversion method in an efficient and accuracy way. It shows that in contrast to idiosyncratic factors, the effect of systematic factors on vulnerable options is strongly affected by the skewness and leptokurtosis features of systematic variance gamma processes. [ABSTRACT FROM AUTHOR]

Given a separable and real Hilbert space H , we consider the following stochastic differential equation (SDE) on H : d X t = − X t d t + b (X t) d t + d Z t , where Z : = (Z t) t ≥ 0 is a cylindrical pure jump Lévy process on H which may be degenerate in the sense that the support of Z is contained in a finite dimensional space. When the nonlinear drift term b (x) is contractive with respect to some proper modified norm of H for large distances, we obtain explicit exponential contraction rates of the SDE above in terms of Wasserstein distance under mild assumptions on the Lévy process Z. The approach is based on the refined basic coupling of Lévy noises, and it also works well when the so-called Lyapunov condition is satisfied. [ABSTRACT FROM AUTHOR]

We discuss the joint calibration to SPX and VIX options of an affine Stochastic Volatility model with Jumps in price and Jumps in volatility (the SVJJ model). Conventionally, the SVJJ model assumes exponential jumps in the variance process, leaving the potential benefits of more flexible jump distributions unexplored. The purpose of our study is twofold. First, we show that choosing the gamma distributions for the jumps in variance significantly improves the performance of the joint calibration. However, this improvement comes at the cost of increased computational time. Second, we mitigate this loss of tractability by constructing novel approximations to option prices based on orthogonal polynomial expansions. Unlike the classical method of selecting an explicit reference density, our approach generalizes to all densities with explicit Laplace transform. We apply this methodology to the SVJJ model with gamma jumps and we find that the proposed price expansions achieve the same accuracy as exact transform inversion formulas while requiring only a fraction of the computational time. [ABSTRACT FROM AUTHOR]

This paper focuses on applying the Corcione model to the microchannel. The Corcione model is highly relevant because it provides accurate empirical relationships for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. These qualities are crucial for building and improving different thermal systems. The model presents and discusses two simple empirical correlating equations for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. Hence the aim of this work is to use Corcione’s model to demonstrate the fully developed laminar flow of an electrically conducting nanoliquid through an inclined microchannel. The energy equation takes into account the physical impacts of the heat source/sink, temperature jamp, and viscous dissipation. TiO2 nanoparticles in water are taken into consideration in this work for enhanced cooling. Using the numerical program Maple, Runge–Kutta–Fehlberg 4th–5th-order method is utilized to solve the present research. Making use of graphs, all of the flow parameters are shown, and the physical consequences on the flow and temperature profiles are thoroughly examined. It is noted that a higher inclined angle enhances the velocity profile whereas a larger temperature jump declines the temperature profile. Furthermore, Corcione’s model often has greater velocities, temperatures, and reduced surface drag forces than the Tiwari–Das model. [ABSTRACT FROM AUTHOR]

This study focuses on the issue of asynchronous observer-based H∞ control for Roesser model-based Two-dimensional Markov jump systems. The goal is to develop an asynchronous controller based on observer so that the system maintains asymptotic mean square stability while exhibiting H∞ disturbance attenuation performance. The asynchrony between the observer and the control plant is described by a hidden Markov process. Furthermore, applying the the Lyapunov function method, a prerequisite for achieving asymptotic mean square stability in closed-loop systems, while maintaining a predefined level of H∞ disturbance attenuation performance, is derived. Based on this criterion, a methodology for designing the intended controller is constructed through the utilization of linear matrix inequalities. The applicability of this scheme is illustrated by the thermal process model with Markov jump parameters. [ABSTRACT FROM AUTHOR]

In this present paper, the event-triggered sliding mode control (SMC) issue for a type of singular networked Markov jump systems with partly unknown transition probabilities (TPs) is mainly investigated, and it is modeled by discrete-time Takagi–Sugeno fuzzy systems. To save network resources, a mode-dependent event-triggered scheme (ETS) is applied to improve transmission efficiency. Subsequently, a common sliding surface is designed, which can effectively reduce the impact of the jumping process. Therein, the stochastic admissibility criterion for the system with H ∞ performance γ is derived in the sense of partly unknown TPs. Moreover, a novel SMC law that guarantees the reachability of the quasi-sliding mode is given in view of the reaching condition. Finally, the validity of the presented theorems is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

We propose a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the generator matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The maximum likelihood (ML) estimates of the mixture's parameters are obtained from continuous realizations of the mixture process and their standard errors from an explicit form of the observed Fisher information matrix, which simplifies the Louis (Journal of the Royal Statistical Society Series B, 44:226–233, 1982) general formula for the same matrix. The asymptotic properties of the ML estimators are also derived. A simulation study verifies the estimates' accuracy. The proposed mixture provides an exploratory tool for identifying the homogeneous subpopulations in a heterogeneous population. This is illustrated with an application to a medical dataset. [ABSTRACT FROM AUTHOR]

We provide an overview of continuous-time processes subject to jumps that do not originate from a compound Poisson process, but from a compound Hawkes process. Such stochastic processes allow for a clustering of self-exciting jumps, a phenomenon for which empirical evidence is strong. Our presentation, which omits certain technical details, focuses on the main ideas to facilitate applications to stochastic control theory. Among other things, we identify the appropriate infinitesimal generators for a set of problems involving various (possibly degenerate) cases of diffusions with self-exciting jumps. Compared to higher-dimensional diffusions, we note a degeneracy of the second-order infinitesimal generator. We derive a Feynman-Kac Theorem for a dynamic system driven by such a jump diffusion and also discuss a problem of continuous control of such a system and provide a verification theorem establishing a link between the value function and a novel type of Hamilton-Jacobi-Bellman (HJB) equation. [ABSTRACT FROM AUTHOR]

Abstract.Under the comprehensive model of assets which satisfy the triple conditions of stochastic jump, stochastic volatility, and stochastic interest rate, the pricing problem of reset options with default risk is investigated. First, two-dimensional log-normal distribution and radical process with reverting property are applied to describe sudden jump of assets and time-varying characteristics of volatility and interest rate, respectively. Further, through the principle of risk neutral pricing with the characteristic function method, we establish the joint characteristic function related to the options. Second, according to measure transform and payoff function decomposition, the analytical pricing and hedging share formulas of vulnerable reset options are given. Third, 3-D fast Fourier transform is constructed to obtain a fast and asymptotic solution of option prices. Finally, the accuracy and stability of 3-D fast Fourier transform is analyzed through numerical examples. The experimental results show that the proposed method can solve the complex pricing problem of vulnerable reset options more efficiently. [ABSTRACT FROM AUTHOR]

The advances in research on the explosion load characteristics of the fuel–air mixture in vented chambers are reviewed herein. The vented explosion loads are classified into three typical types based on this comprehensive literature research. These models are the accumulation load model, attenuation load model, and interval jump load model. The characteristics of the three different typical vented explosion load models are analyzed using Fluidy-Ventex. The research results show that overpressure is largely determined by methane concentrations and vented pressure. The turbulent strength increased from the original 0.0001 J/kg to 1.73 J/kg, which was an increase of 17,300 times, after venting in the case of a 10.5 v/v methane concentration and 0.3 kPa vented pressure. When the vented pressure increased to 7.3 kPa, the turbulent strength increased to 62.2 J/kg, and the overpressure peak correspondingly increased from 69 kPa to 125 kPa. In the case of the interval jump load model, the explosion overpressure peak tends to ascend when the intensity of the fluid disturbance rises due to the venting pressure increasing at a constant initial gas concentration. When the venting pressure reaches tens of kPa, the pressure differential increases sharply on both sides of the relief port, and a large amount of combustible gas is released. Therefore, there is an insufficient amount of indoor combustible gas, severe combustion is difficult to maintain, and the explosion load mode becomes the attenuation load model. [ABSTRACT FROM AUTHOR]

In this paper, we construct the reweighted Nadaraya–Watson estimators of the infinitesimal moments for the volatility process of the stochastic volatility models, with the application of the threshold estimator of the unobserved volatility process. Our model includes jumps in both the underlying asset price and its volatility process. We derive the asymptotic properties of the estimators under the infill and long span assumptions. The results are useful for identification of the process. The finite-sample performance of the estimators is studied through Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

AbstractWe derive a new fractional Heston model with self-exciting jumps. We study volatility persistence and demonstrate that the quadratic variation necessarily exhibits less memory than the integrated variance, which preserves the degree of long-memory of the instantaneous volatility. Focusing on realized volatility measures, we find that traditional long-memory estimators are dramatically downward biased, in particular for low-frequency intraday sampling. Conveniently, our Monte Carlo experiments reveal that some noise-robust local Whittle-type estimators offer good finite sample properties. We apply our theoretical results in a risk forecasting study and show that our frequency-domain forecasting procedure outperforms the traditional benchmark models. [ABSTRACT FROM AUTHOR]

Both Markovian and arbitrary residence time distributions are considered. The comparison of analytical predictions with the case of a time-decorrelated process shows that correlations can both decrease and increase the corresponding expected waiting time. Besides, the comparison of exponential, subexponential, and heavy-tailed models characterized by equal probabilities to observe the event of interest demonstrates that a faster decrease in the residence time probability density implies a shorter expected waiting time. Interestingly, irrespective of the details of a particular model for both discrete- and continuous-time jump processes considered here, the random waiting time becomes exponentially distributed in the long-time limit, thus, showing remarkable universality. [ABSTRACT FROM AUTHOR]

In this article, we study the merging and splitting of generalized counting processes (GCPs). First, we study the merging of a finite number of independent GCPs and then extend it to the case of countably infinite. The merged process is observed to be a GCP with increased arrival rates. It is shown that a packet of jumps arrives in the merged process according to the Poisson process. Also, we study two different types of splitting of a GCP. In the first type, we study the splitting of jumps of a GCP where the probability of simultaneous jumps in the split components is negligible. In the second type, we consider the splitting of jumps in which there is a possibility of simultaneous jumps in the split components. It is shown that the split components are GCPs with certain decreased jump rates. Moreover, the independence of split components is established. Later, we discuss applications of the obtained results to industrial fishing problem and hotel booking management system. [ABSTRACT FROM AUTHOR]

In this paper, we develop a 'jump diffusion type' financial model based on renewal processes for the discontinuous part of the risk driver, and study its ability to price options and accurately reproduce the corresponding implied volatility surfaces. In this model, the log-returns process displays finite mean and variance, and non-vanishing skewness and excess kurtosis over a long period. The proposed construction is parsimonious, and it allows for a simple and intuitive pricing formula for European vanilla options; furthermore, it offers an efficient Monte Carlo sample path generator for the pricing of exotic options. We illustrate the performance of the proposed framework using observed market data, and we study the features of the best fitting model specifications. [ABSTRACT FROM AUTHOR]

Efficient and effective modeling of complex systems, incorporating cloud physics and precipitation, is essential for accurate climate modeling and forecasting. However, simulating these systems is computationally demanding since microphysics has crucial contributions to the dynamics of moisture and precipitation. In this paper, appropriate stochastic models are developed for the phase-transition dynamics of water, focusing on the precipitating quasi-geostrophic (PQG) model as a prototype. By treating the moisture, phase transitions, and latent heat release as integral components of the system, the PQG model constitutes a set of partial differential equations (PDEs) that involve Heaviside nonlinearities due to phase changes of water. Despite systematically characterizing the precipitation physics, expensive iterative algorithms are needed to find a PDE inversion at each numerical integration time step. As a crucial step toward building an effective stochastic model, a computationally efficient Markov jump process is designed to randomly simulate transitions between saturated and unsaturated states that avoids using the expensive iterative solver. The transition rates, which are deterministic, are derived from the physical fields, guaranteeing physical and statistical consistency with nature. Furthermore, to maintain the consistent spatial pattern of precipitation, the stochastic model incorporates an adaptive parameterization that automatically adjusts the transitions based on spatial information. Numerical tests show the stochastic model retains critical properties of the original PQG system while significantly reducing computational demands. It accurately captures observed precipitation patterns, including the spatial distribution and temporal variability of rainfall, alongside reproducing essential dynamic features such as potential vorticity fields and zonal mean flows. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid numerical method for simulating the boiling heat transfer in particle-laden fluids. The coupled volume of fluid and level set method, immersed boundary method, and discrete element method are integrated for gas–liquid flow, fluid–solid interaction, and the collision between particles. The energy jump model is adopted to compute mass transfer during phase change. The height-function technique and improved continuum surface force (CSF) model are coupled to decrease the spurious currents. Multiple validation results are provided to test the effectiveness of all sub-models. The test cases include particle sedimentation, stationary droplets without gravity, bubble rise, droplet spreading on particle surfaces, and bubble growth. The test results are in good agreement with analytical results and previous studies. Notably, the average spurious velocity is reduced to less than 10−5 m/s, which is three orders of magnitude smaller than that obtained by traditional CSF model. Moreover, the hybrid method is employed to explore the boiling heat transfer of particle-laden fluids, thereby further validating its reliability. It was found that particles facilitate bubble detachment and enhance heat transfer. [ABSTRACT FROM AUTHOR]

Legged robots offer advantages such as rapid mobility, adept obstacle-surmounting capabilities, and long mission life in lunar exploration missions. The low-gravity environment on the Moon enhances these benefits, particularly in enabling efficient jumps. However, challenges arise from the complexity of the jumping motion and the difficulty in maintaining stability. This paper introduces an innovative algorithm that integrates deep reinforcement learning with a main point trajectory generator, thus providing a reference for training with minimal reliance on human intuition and prior knowledge. Additionally, fine-grained policy optimization is achieved through a multistage reward structure based on the decomposition of the jumping process. Further, the concept of multitask experience-sharing is proposed to facilitate efficient learning across tasks involving plain terrain jumping and overcoming large obstacles. Simulation results demonstrate the effectiveness of the proposed algorithm in achieving precise and stable jumps, reaching heights approximately five times the robot's height and distances over five times its body length under lunar gravity. Moreover, the robot exhibits agile strategies, successfully overcoming platforms with a height of 2.5 times its body. [ABSTRACT FROM AUTHOR]

This paper proposes a novel asymmetric jump model for modeling interactions in discontinuous movements in asset prices. Given the jump behavior and high volatility levels in cryptocurrency markets, we apply our model to cryptocurrencies to study the impact of various types of jumps occurring in one cryptocurrency's price process on the discontinuity component of the realized volatility of other cryptocurrencies. Our model also allows us to assess the impact of co-jumps. Using high-frequency data to compute the daily realized volatility, we show that downside, upside, and small jumps observed in cryptocurrencies negatively affect the jump component of other cryptocurrencies' realized volatility, while large jumps have the opposite effect. We further find significant asymmetric effects between small and large as well as between downside and upside jumps for several cryptocurrencies. Moreover, we find evidence of co-jumping behavior, which can trigger future jumps. The practical implications of our findings are also discussed. Finally, we extend our analysis to study the effects of jumps in mainstream financial assets on cryptocurrencies' jump behavior and find that upside and downside jumps observed in the S&P 500 index negatively impact cryptocurrency jumps. [ABSTRACT FROM AUTHOR]

The erosion‐deposition propagation of granular avalanches is prevalent and may increase their destructiveness. However, this process has rarely been reported for debris flows on gentle slopes, and the contribution of momentum hidden under the surge front to debris‐flow destructiveness is ambiguous. Therefore, the momentum carried by the apparent surge front is often used to indicate debris‐flow destructiveness. In this study, the erosion‐deposition propagation is confirmed by surge‐depth hydrographs measured at the Jiangjia Ravine (Yunnan Province, China). Based on simple hydraulic jump equations, the eroded deposition depth of surge flow is quantified, and the erosion pattern can be divided into two patterns (shallow and deep erosion). For surge flows with erosion‐deposition propagation, significant downward erosion potential is confirmed, and debris‐flow surge erosion is considered the deep erosion. The total momentum carried by surge flow is further quantified by two Froude numbers (surge‐front and rearward Froude numbers) and verified through the field observation of surge flows. The total momentum of surge flow not only originates from the apparent surge front, but also includes the momentum within the eroded deposition layer. This study provides a theoretical approach for quantifying the upper limit of erosion depth and revealing the destructiveness of debris‐flow surges. A perspective on the importance of substrate deposition for debris‐flow erosion on gentle slopes is emphasized, as this approach can improve the reliability of debris‐flow risk assessment. Plain Language Summary: For flow‐type mass movements consisting of multiple surges, a subsequent surge would entrain the deposition of previous surges. The subsequent surge continues to move forward until it deposits again. This deposition is in turn carried away by the subsequent surges. This process is termed erosion‐deposition propagation. The erosion‐deposition propagation widely occurs in snow avalanches and enhances destructiveness by amplifying the scale and mobility of avalanches. For debris flows on gentle slopes, erosion‐deposition propagation has not been reported, and the effect of this process on debris‐flow destructiveness is unclear. In this study, the erosion‐deposition propagation of debris flows is confirmed by the field observation of surge flows at the Jiangjia Ravine (Yunnan Province, China). Based on simple hydraulic jump equations, the erosion into deposition of surge flow is quantified. The erosion patterns and momentum hidden under debris‐flow surges are revealed. The deep erosion pattern means that the apparent debris‐flow surge is merely "the tip of the iceberg," and there is a large portion underneath. This study proposes a theoretical approach for quantifying the eroded deposition depth and the total momentum carried by debris‐flow surges, which is conducive to a precise risk assessment and mitigation of debris‐flow surges. Key Points: The erosion‐deposition propagation of debris flow is confirmed by surge‐depth hydrographs measured at the Jiangjia Ravine, Yunnan Province, ChinaShallow and deep erosion patterns are revealed by hydraulic jump equations. The debris‐flow surges at the Jiangjia Ravine fall into the deep erosionThe destructiveness of debris‐flow surges is quantified by considering the momentum hidden under the surge front and confirmed by field observation [ABSTRACT FROM AUTHOR]

For continuous‐time complex‐valued neural networks, this paper addresses the state‐feedback stabilization issue via dynamic event‐triggered protocol. Aiming at random parameters' switching, semi‐Markov jump model surpasses the Markov jump model in terms of its generality, enabling us to effectively capture the occurrence of random abrupt alterations in both the structure and parameters of complex‐valued neural networks. To optimize packet transmission, a new dynamic event‐based protocol is introduced to judge whether the previous signal transmission continues. The design of this protocol takes into full consideration the imaginary part characteristics of the system, while also integrating the system modes and dynamic variables. Utilizing an appropriate Lyapunov functional that contains auxiliary internal dynamical variables, the desired stability is proposed. Eventually, the effectiveness of theoretical findings is ultimately validated through two numerical simulations. [ABSTRACT FROM AUTHOR]

This article investigates the optimal excess-loss reinsurance, investment, and the rationality of using a diffusion model to approximate a jump model. We assume that the instantaneous rate of return of the risky asset is modelled by an Ornstein-Uhlenbeck (O-U) process, and the insurance claims are modeled by a compound Poisson (CP) process and a diffusion approximation (DA) model. By using the stochastic dynamic programming method, the closed-form expressions for the optimal reinsurance and investment strategies and the corresponding value functions are derived. We find that the insurer with the CP claim model always has higher reinsurance demand than the insurer with the DA claim model. Moreover, the error of using the DA model to approximate the CP model is very much dependent on the reinsurance price. Numerical analysis shows that the insurer adjusts the investment strategy as the state of the financial market changes. [ABSTRACT FROM AUTHOR]

This article studies the joint ruin problem for two insurance companies that divide claims in positive proportions (modeling an insurance and re-insurance company). The arrival times of claims are delayed by a common random time. Suppose that the two insurance companies are allowed to make risk-free and risky investments, and the price processes of the corresponding investment portfolios are exponentials of jump-diffusion processes with common jumps. Furthermore, assuming that the claim sizes and their corresponding investment return jump possess a dependence structure, this article establishes an asymptotic formula for the ruin probability. [ABSTRACT FROM AUTHOR]

We discuss via general arguments and examples when and why the steady nonequilibrium heat capacity vanishes with temperature. The framework is that of Markov jump processes on finite connected graphs where the condition of local detailed balance allows to identify the heat fluxes, and where the discreteness more easily enables sufficient nondegeneracy of the stationary distribution at absolute zero, as under equilibrium. However, for the nonequilibrium extension of the Third Law of Thermodynamics, a dynamic condition is needed as well: the low-temperature dynamical activity and accessibility of the dominant state must remain sufficiently high so that relaxation times do not start to dramatically differ between different initial states. It suffices that the relaxation times do not exceed the dissipation time. [ABSTRACT FROM AUTHOR]

The valuation of equity-linked annuity (EIA) has been extensively studied, while few papers consider the impact of long-range dependence (LRD) features on financial and mortality dynamics in EIAs' valuation. To characterise the LRD feature, we adopt the fractional Brownian motion (FBM) in modelling the dynamics of asset prices and mortality intensities, in which clustering jumps are captured by the compound Hawkes process. Besides, the interest rate dynamic is driven by the FBM and correlates to the asset price dynamic. Numerical analyses show that ignorance of the LRD feature and the jump component in the modelling framework could lead to a potential deficiency in the reserve and solvency capital of EIA policies. [ABSTRACT FROM AUTHOR]

This paper focuses on the pricing problem of binary options under stochastic interest rates, stochastic volatility, and a mixed exponential jump diffusion model. Considering the negative interest rates in the market in recent years, this paper assumes that the stochastic interest rate follows the Hull–White (HW) model. In addition, we assume that the stochastic volatility follows the Heston volatility model, and the price of the underlying asset follows the jump diffusion model in which the jumps follow the mixed exponential jump model. Considering these factors comprehensively, the mixed exponential jump diffusion of the Heston–HW (abbreviated as MEJ-Heston–HW) model is established. Using the idea of measure transformation, the pricing formula of binary call options is derived by the martingale method, eigenfunction, and Fourier transform. Finally, the effects of the volatility term and the parameters of the mixed-exponential jump diffusion model on the option price in the O-U process are analyzed. In the numerical simulation, compared with the double exponential jump Heston–HW (abbreviated as DEJ-Heston–HW) model and the Heston–HW model, the mixed exponential jump model is an extension of the double exponential jump model, which can approximate any distribution in the sense of weak convergence, including arbitrary discrete distributions, normal distributions, and various thick-tailed distributions. Therefore, the MEJ-Heston–HW model adopted in this paper can better describe the price of the underlying asset. [ABSTRACT FROM AUTHOR]

We study the clustering behavior of stock return jumps modeled by a self/cross-exciting process embedded in a stochastic volatility model. Based on the model estimates, we propose a novel measurement of stock price efficiency characterized by the extent of jump clustering that stock returns exhibit. This measurement demonstrates the capability of capturing the speed at which stock prices assimilate new information, especially at the firm-specific level. Furthermore, we assess the predictability of self-exciting (clustered) jumps in stock returns. We employ a particle filter to sample latent states in the out-of-sample period and perform one-step-ahead probabilistic forecasting on upcoming jumps. We introduce a new statistic derived from predicted probabilities of positive and negative jumps, which has been shown to be effective in return predictions. [ABSTRACT FROM AUTHOR]

This article addresses the static output feedback load frequency control (LFC) problem for semi‐Markov type interconnected multi‐area power systems (IMAPSs) through non‐fragile proportional‐integral (PI) strategy. Primarily, by roundly exploiting the dynamical properties and considering random mutations of the IMAPSs, the semi‐Markov jump process (MJP) is elaborately scheduled for establishing the dynamical model with precision. Subsequently, on account of the characteristic of geographical isolation, a memory‐like sampled‐data LFC mechanism considering time‐varying transmission delay for the semi‐Markov jump IMPASs is formulated accordingly. Additionally, the non‐fragile issue is explored for the PI controller gain fluctuations to meet the actual operation scenario. After that, a mode‐dependent two‐side polynomial‐type looped Lyapunov functional is constructed for enhancing flexibility. Then, in virtue of the stochastic analysis technique, some relaxed conditions guaranteeing stochastic stability with prescribed H∞$$ {H}_{\infty } $$ performance are thereby derived in the shape of linear matrix inequalities (LMIs). Ultimately, a numerical example is carried out to validate the efficacy of the developed control methodology. [ABSTRACT FROM AUTHOR]

Ferroelectric (FE) materials and their advancements have piqued the scientific community's interest greatly since they provide numerous fascinating processes in addition to being used in devices. Among them, we have studied Mn and Sn co-doped PZT and Pb (Zr0.52Ti0.48) O3 as PZT, an extremely intriguing FE. The structure and phase purity of all the samples are determined by x-ray diffraction techniques. All the samples show a very good microstructures and the average grain size is found to be decreased with ion incorporation. The UV-Vis spectra show how doping reduces optical band gaps. Parallel resistance (R)-capacitance (C) circuits have been used to analyze the relationship between microstructure and electrical characteristics. The microscopic processes in various PZT samples with dilute magnetic cations at A-sites, B-sites, and/or both sites at the morphotopic phase boundary are established from the detail impedance, modulus, and ac conductivity of the samples as a function of temperature (300 –500 °C) and over a range of frequency (100 Hz to 1 MHz). Additionally, the framework of the Jump relaxation model and the Jonscher power law are used to study the ac-conductivity data. [ABSTRACT FROM AUTHOR]

This article explores pure-endowment contracts with investments that are simultaneously allocated in risk-free and risky financial markets. Employing the optimal stochastic control method and assuming that the jumps of the risky financial market follow either a finite or infinite activity Lévy process, and that the policyholder's utility function is a Constant Relative Risk Aversion (CRRA) utility function, the article derives an optimal investment strategy and optimal policyholder consumption, with dependency on the mortality rate. Various mortality models and jump parameters are utilized to investigate the sensitivity of our findings. Finally, the article establishes the fair price of such contracts under different circumstances, showcasing practical applications through several examples. [ABSTRACT FROM AUTHOR]

For two Polish state spaces E X and E Y , and an operator G X , we obtain existence and uniqueness of a G X -martingale problem provided there is a bounded continuous duality function H on E X × E Y together with a dual process Y on E Y which is the unique solution of a G Y -martingale problem. For the corresponding solutions (X t) t ≥ 0 and (Y t) t ≥ 0 , duality with respect to a function H in its simplest form means that the relation E x [ H (X t , y) ] = E y [ H (x , Y t) ] holds for all (x , y) ∈ E X × E Y and t ≥ 0. While duality is well-known to imply uniqueness of the G X -martingale problem, we give here a set of conditions under which duality also implies existence without using approximating sequences of processes of a different kind (e.g. jump processes to approximate diffusions) which is a widespread strategy for proving existence of solutions of martingale problems. Given the process (Y t) t ≥ 0 and a duality function H , to prove existence of (X t) t ≥ 0 one has to show that the r.h.s. of the duality relation defines for each y a measure on E X , i.e. there are transition kernels (μ t) t ≥ 0 from E X to E X such that E y [ H (x , Y t) ] = ∫ μ t (x , d x ′) H (x ′ , y) for all (x , y) ∈ E X × E Y and all t ≥ 0. As examples, we treat resampling and branching models, such as the Fleming–Viot measure-valued diffusion and its spatial counterparts (with both, discrete and continuum space), as well as branching systems, such as Feller's branching diffusion. While our main result as well as all examples come with (locally) compact state spaces, we discuss the strategy to lift our results to genealogy-valued processes or historical processes, leading to non-compact (discrete and continuum) state spaces. Such applications will be tackled in forthcoming work based on the present article. [ABSTRACT FROM AUTHOR]

• A novel degradation process with abrupt jumps caused by operation state transition is proposed. • Analytical reliability solutions of the model are derived in the form of one-dimensional Laplace-Stieltjes transform. • The limit reliability solutions are investigated, as alternative strategy under long-term service. • Analytical solutions regarding statistical characteristics of degradation amount during regeneration epoch are proposed. • The case of spool valve is implemented to verify the effectiveness and the feasibility of the solutions. This paper proposes a novel type of degradation process incorporating continuous degradation and abrupt degradation jump under dynamic operation states. By analyzing the failure mechanism of practical application, the abrupt degradation jump is comprehensively considered, and it is triggered by some certain state switching processes. Then, the reliability solutions of the degradation process (reliability function and moments of lifetime) are derived in the form of Laplace-Stieltjes transform. To a further step, inspired by the advanced equipment with long service span, the reliability solutions in limit region are explored, where an effective calculation method regarding statistical characteristics of degradation amount during regeneration epoch is pioneeringly proposed. To verify the proposed solutions in the form of Laplace-Stieltjes transform and their limit case, the representative example, spool valve, is implemented, and the results show the effectiveness and the feasibility of the solutions. [ABSTRACT FROM AUTHOR]

Energy dissipation of water flow is an important factor in the planning of structures such as stilling basins. One of the standards set by the USBR (United States Bureau of Reclamation) that must be considered in the planning of the stilling basin is the Froude number (F1) at the toe of the spillway. Various forms of planning can be used to meet these standards, one of which is by using a double-sill downstream of the chute channel with a certain distance and height. However, as an alternative to planning, this study aims to evaluate the level of attenuation of flow energy in a stilling basin by using a double-sill. Because this sill is more effective in breaking down and reducing the strength of the water flow. Hydraulic physical model tests were carried out in the laboratory by placing double sills in a fixed position and varying the height of the sills. Because several previous studies have shown that the shape and size of sills affect the level of energy dissipation. It is expected that the results of the hydraulic model test can provide better information about the flow behavior in the overflow system in terms of energy dissipation. [ABSTRACT FROM AUTHOR]

In this article, to model risk contagion between the U.S. and China stock markets based on high-frequency financial data, we develop a novel continuous-time jump-diffusion process. For example, we consider three channels for volatility contagion—such as integrated volatility, positive jump variation, and negative jump variation—and each stock market is able to affect the other stock market as an overnight risk factor. We develop a quasi-maximum likelihood estimator for model parameters and establish its asymptotic properties. Furthermore, to identify contagion channels and test the existence of a structural break with a known structural break date, we propose hypothesis test procedures. Using the proposed diffusion model with high-frequency financial data, we investigate the effect of the U.S.–China trade war on stock markets from a financial contagion perspective. From the empirical study, we find evidence of financial contagion from the United States to China and evidence that the risk contagion channel has changed from integrated volatility to negative jump variation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate fade-in options under GARCH-jump processes. Specifically, we adopt NIG distributions to capture jump risk, and both market and individual jumps are considered. In the pricing model driven by GARCH-jump processes, we obtain the prices of fade-in options using the Fourier transform methods. Finally, we use the derived pricing formulae to illustrate the effects of fade-in sets and the parameters in the jump processes. [ABSTRACT FROM AUTHOR]

We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes‐type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier‐Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati‐Volterra equations, which can be efficiently approximated using a multi‐factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self‐exciting jumps in order to capture the joint evolution of the S&P 500 and VIX. [ABSTRACT FROM AUTHOR]

Stochastic modelling of fatigue (and other material's deterioration), as well as of cumulative damage in risk theory, are often based on compound sums of independent random variables, where the number of addends is represented by an independent counting process. We consider here a cumulative model where, instead of a renewal process (as in the Poisson case), a linear birth (or Yule) process is used. This corresponds to the assumption that the frequency of "damage" increments accelerates according to the increasing number of "damages". We start from the partial differential equation satisfied by its transition density, in the case of exponentially distributed addends, and then we generalize it by introducing a space derivative of convolution type (i.e., defined in terms of the Laplace exponent of a subordinator). Then we are concerned with the solution of integro‐differential equations, under proper initial conditions, which, in a special case, reduce to a fractional one. Correspondingly, we analyze the related cumulative jump processes under a general infinitely divisible distribution of the (positive) jumps. Some special cases (such as the stable, tempered stable, gamma, and Poisson) are presented. [ABSTRACT FROM AUTHOR]

The emergence of multi-disease epidemics presents an escalating threat to global health. In response to this serious challenge, we present an innovative stochastic susceptible–vaccinated–infected–recovered epidemic model that addresses the dynamics of two diseases alongside intricate vaccination strategies. Our novel model undergoes a comprehensive exploration through both theoretical and numerical analyses. The stopping time concept, along with appropriate Lyapunov functions, allows us to explore the possibility of a globally positive solution. Through the derivation of reproduction numbers associated with the stochastic model, we establish criteria for the potential extinction of the diseases. The conditions under which one or both diseases may persist are explained. In the numerical aspect, we derive a computational scheme based on the Milstein method. The scheme will not only substantiate the theoretical results but also facilitate the examination of the impact of parameters on disease dynamics. Through examples and simulations, we have a crucial impact of varying parameters on the system's behavior. [ABSTRACT FROM AUTHOR]

Let us consider a two-sided multi-species stochastic particle model with finitely many particles on Z , defined as follows. Suppose that each particle is labelled by a positive integer l, and waits a random time exponentially distributed with rate 1. It then chooses the right direction to jump with probability p, or the left direction with probability q = 1 − p . If the particle chooses the right direction, it jumps to the nearest site occupied by a particle l ′ < l (with the convention that an empty site is considered as a particle with labelled 0). If the particle chooses the left direction, it jumps to the next site on the left only if that site is either empty or occupied by a particle l ′ < l , and in the latter case, particles l and l ′ swap their positions. We show that this model is integrable, and provide the exact formula of the transition probability using the Bethe ansatz. [ABSTRACT FROM AUTHOR]