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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]

In this study, we model aggregate claims using a subordinator, specifically a non-decreasing Lévy process. Large positive jumps, exceeding a predetermined threshold, represent significant claims, while frequent but smaller fluctuations capture other sources of non-insurance uncertainty, such as miscellaneous expenses. The primary challenge lies in extracting the necessary mathematical insights to estimate the jump measure from a sample path of truncated aggregate claims. Through a discrete time-point sampling scheme, we conduct an initial comparison between conventional parametric estimators of the Lévy measure associated with the subordinator, based on simulated significant claims, and our proposed non-parametric estimator, derived by adapting classical differential processes originally introduced by Rubin and Tucker. The results of this comparison suggest the potential utility of our estimator in the context of real data from the insurance sector. While the primary focus of this work is to uncover the mathematical foundations, a preliminary simulation study, although lacking rigorous numerical analysis, hints at the favorable estimation of the Poisson rate for the number of jumps exceeding the threshold, achieved using our proposed non-parametric estimator of the Lévy measure. [ABSTRACT FROM AUTHOR]

Abstract.The data distributions of many financial and econometric sequences always exhibit heavy-tailed phenomena, which trigger distinct difficulty in parameter estimation by classical least squares method. This article aims to construct a new ratio-typed test based on least absolute deviation estimation that effectively circumvents the problem of long-run variance estimation and has robustness on detecting structural changes under strong mixing sequences with heavy-tailed innovations. This is because the least absolute deviation estimation can allow for processes within the domain of attraction of a stable law with an index κ∈(0,2), not limited to (1, 2). Under some regular conditions, the asymptotic distribution under the null hypothesis is derived as a functional of Brownian motion, not a functional of lévy process, and the divergence rate under the alternative hypothesis is also provided. Furthermore, the consistency of a ratio-typed change point estimator is given and its convergence rate is established. The numerical simulation indicates that empirical sizes are undistorted, and empirical powers exhibit significant performance. Finally, two practical application examples are presented to illustrate the validity of the proposed test procedures. [ABSTRACT FROM AUTHOR]

To achieve the optimal solution between construction costs and carbon emissions in the multi-target optimization scheduling, this paper proposes a multi-objective optimization scheduling design for wind–solar energy storage microgrids based on an improved oppositional gradient grey wolf optimization (OGGWO) algorithm. First, two new features were added to the traditional grey wolf optimization (GWO) algorithm to solve the multi-target optimization scheduling of grid-connected microgrids, aiming to improve solution quality and convergence speed. Furthermore, Gaussian walk and Lévy flight are introduced to enhance the search capability of the proposed OGGWO algorithm. This method expands the search range while sacrificing only a small amount of search speed, contributing to obtaining the global optimal solution. Finally, the gradient direction is considered in the feature search process, allowing for a comprehensive understanding of the search space, which facilitates achieving the global optimum. Experimental results indicate that, compared to traditional methods, the proposed improved OGGWO algorithm can achieve standard deviations of 4.88 and 4.46 in two different scenarios, demonstrating significant effectiveness in reducing costs and pollution. [ABSTRACT FROM AUTHOR]

In order to solve the problem of poor adaptability and robustness of the rule-based energy management strategy (EMS) in hybrid commercial vehicles, leading to suboptimal vehicle economy, this paper proposes an improved dung beetle algorithm (DBO) optimized multi-fuzzy control EMS. First, the rule-based EMS is established by dividing the efficient working areas of the methanol engine and power battery. The Tent chaotic mapping is then used to integrate strategies of cosine, Lévy flight, and Cauchy Gaussian mutation, improving the DBO. This integration compensates for the traditional dung beetle algorithm's tendency to fall into local optima and enhances its global search capability. Subsequently, fuzzy controllers for the driving charging mode and hybrid driving mode are designed under this rule-based EMS. Finally, the improved DBO is used to obtain the optimal control of the fuzzy controller by taking the fuel consumption of the whole vehicle and the fluctuation change of the battery state of charge (SOC) as the optimization objectives. Compared to traditional rule-based energy management strategies, the optimized fuzzy control using the enhanced DBO continuously adjusts the torque distribution between the engine and motor based on the vehicle's real-time state, resulting in a 9.07% reduction in fuel consumption and a 3.43% decrease in battery SOC fluctuations. [ABSTRACT FROM AUTHOR]

In the framework of contemporary power systems, a distributed generation (DG) system has benefits, but it also presents several operational challenges. In a networked distributed generation system, islanding is one such problem. Because of the negative consequences, an islanding event should be distinguished from other events, like transients within the minimum time. A multi-level adaptive neuro-fuzzy inference system (ANFIS) is being developed in this work to effectively detect islanding. To train the ANFIS model, a novel hybrid scheme based on Lévy flights and teaching–learning-based optimiser is suggested. The performance of the developed algorithm is evaluated using the IEEE CEC-C06 and other traditional benchmark functions. The ANFIS model's classification regime is significantly improved by the optimisation algorithm. In the test system, renewable energy sources are used to power a voltage source converter unit in a network-forming mode via an energy storage medium. Based on measured frequency, RMS voltage and current, active and reactive power, voltage, and current THD at the point of common coupling (PCC), the trained ANFIS controller deduces the islanding detection command to the circuit breaker. The plan is verified following the UL1741 standard for islanding prevention, yielding notable outcomes with an average detection time of 0.04s and an accuracy of 89.3%. [ABSTRACT FROM AUTHOR]

We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable Lévy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of Ornstein-Uhlenbeck processes. However, unlike Ornstein-Uhlenbeck processes with a tempered stable driver exact transition probabilities for higher order CARMA processes are not explicitly given. Therefore, we use a numerical sample path generation method and approximate the driving tempered stable Lévy process by a truncated series representations. We derive a result of a series representation for p-tempered α-stable distributions. We prove approximation error bounds and conduct Monte Carlo experiments to illustrate the usefulness of the approach. [ABSTRACT FROM AUTHOR]

We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures the market expectations of future volatility, but traditional methods based on second-moment shocks and the time-varying volatility of the VIX often do not effectively to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we constructed a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Lévy process to S&P 500 log returns, to provide a more comprehensive measure of volatility that captures the extreme movements and heavy tails observed in financial data. Using an axiomatic framework, we developed a family of risk–reward ratios that, when computed with our revised VIX and fitted to a long-memory time series model, provide a more precise identification of uncertainty shocks in financial markets. [ABSTRACT FROM AUTHOR]

Structural credit risk modeling is a commonly used risk-management approach for fixed-income, with Lévy models offering more realistic tail behavior than assumed in the classical Merton formulation. This article presents an innovative Esscher-based algorithm for computing default probabilities in structural credit risk models driven by Lévy processes. The algorithm starts by matching the moments of observed equity values to infer model parameters. Using the cumulant generating function, it then computes the risk-neutral characteristic function and derives asset values through inversion of a Fourier option pricing formula. The physical parameters are updated by matching the moments of these asset values, iterating until convergence. As an illustration, the algorithm is applied to multiple issuers with various ratings, and to three Lévy models: Merton, variance gamma, and bilateral gamma. As expected, the Merton model consistently underestimates default probabilities for short maturities; the bilateral gamma model provides more conservative estimates. The empirical analysis demonstrates the robustness of the algorithm across different market conditions, highlighting its ability to provide valuable insights for both academic research and practical risk management. This approach, therefore, offers a complimentary risk-modeling perspective to the traditional Merton framework. For reader's convenience, calibration code is made publicly available. [ABSTRACT FROM AUTHOR]

Engineers and designers working in the aerospace industry are always under pressure to enhance mechanical effectiveness and maximize structural performance. Due to their extreme stiffness and small weight, composite surfaces are often utilized in bending-stress-prone constructions like wings and fuselages. In order to increase the effectiveness of temporary double-curved surfaces under external stresses, we employed high-performance nanocomposites termed graphene nanoplates as reinforcing nanofillers inside polymers. Three-dimensional flexibilities using equilibrium conditions as well as analytical methods are used for developing and solving complex equations. For general modeling of the external mechanical loading, step, triangle, and half-sine loadings to model the current work in a general complex position. The novelties of the current work are considering three-dimensional flexibilities and external mechanical loading for extracting transient responses of doubly curved surfaces under external force. As well as this, with the aid of this analysis, free and forced vibrations of the current structure are shown in the transient response of the doubly curved surface using three-dimensional flexibilities, for the first time. This paper will use a data mining algorithm to optimize the performance of mathematical simulation and use Multi-Objective Grey Wolf with Lévy Flight and Mutation Operator to simulate the system. For this purpose, four thousand five hundred collocation points in the cube and one thousand five hundred boundary points on each boundary surface are produced at random and used as training samples. The results section shows that there is a reduction of up to 45% in displacement when the weight fraction percentage of graphene nanoplate increases from 1% to 4%. Another important outcome is that for all force intensities, the compressive stress induced in the surface is 30% higher in the x direction in comparison with the y direction. Finally, for related industries, it is shown that the curvature ratio decreases from infinity to three, curved surface experiences a reduction of 50% in the shear stress. [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]

The position of the distribution network and its peculiar topology calls for viable means of addressing the issue of severe power loss and voltage instability confronting its ability to truly wheel out the received energy from the transmission arm of the network to the end users. Based on this premise, the current work employed a Lévy flight genetic algorithm (LF-GA) for the placement of type-1 photovoltaic-based distributed generation (PV-DG) into a radial network. The IEEE 33 and Government Residential Area (GRA) 11 kV and 34-bus feeder in Nigeria were used to investigate the effectiveness of the proposed approach. The backward-forward sweep formed the backbone of the load flow, while the voltage stability index was used to select the suitable buses where type-1 DG was integrated for optimal performance. The criteria considered for performance evaluation were the cost of energy loss, payback time, active power loss, and network voltage profile improvement without violating the essential network constraints. The paper proposed a relevant policy framework on DG integration, which filled knowledge gap in the previous studies. A multi-objective factor-based LF-GA subjected to appropriate constraints was used to optimize both the sizing and the locations of type-1 DG with the arrangements implemented in a MATLAB environment. The results obtained when compared with the existing contributions in the literature showed a credible improvement in line-loss reduction, voltage profile, and the system voltage stability index, including reduced cost of energy loss with minimal payback time on the investment of compensating devices. [ABSTRACT FROM AUTHOR]

Many organisms, ranging from modern humans to extinct species, exhibit movement patterns that can be described by Lévy walk dynamics. It has been demonstrated that such behavior enables optimal foraging when resource distribution is sparse. Here, we analyze a dataset of football player trajectories, recorded during the matches of the Japanese football league, to elucidate the presence of statistical signatures of Lévy walks, such as the heavy‐tailed distribution of distances traveled between significant turns and the characteristic superdiffusive behavior. We conjecture that the competitive environment of a football game leads to bursty movement dynamics reminiscent of that observed in hunter‐gathering populations and more broadly in any biological organisms foraging for resources, whose exact distribution is unknown to them. Apart from analyzing individual players' movements, we investigate the dynamics of the whole team by studying the movements of its center of mass (team's centroid). Remarkably, the trajectory of the centroid also exhibits Lévy walk properties, marking the first instance of such type of motion observed at the group level. Our work concludes with a comparative analysis of different teams and some discussion on the relevance of our findings to sports science and science more generally. [ABSTRACT FROM AUTHOR]

Currently, numerous intelligent maximum power point tracking (MPPT) algorithms are capable of tackling the global optimization challenge of multi-peak photovoltaic output power under partial shading conditions, yet they often face issues such as slow convergence, low tracking precision, and substantial power fluctuations. To address these challenges, this paper introduces a hybrid algorithm that integrates an improved salp swarm algorithm (SSA) with the perturb and observe (P&O) method. Initially, the SSA is augmented with a dynamic spiral evolution mechanism and a Lévy flight strategy, expanding the search space and bolstering global search capabilities, which in turn enhances the tracking precision. Subsequently, the application of a Gaussian operator for distribution calculations allows for the adaptive adjustment of step sizes in each iteration, quickening convergence and diminishing power oscillations. Finally, the integration with P&O facilitates a meticulous search with a small step size, ensuring swift convergence and further mitigating post-convergence power oscillations. Both the simulations and the experimental results indicate that the proposed algorithm outperforms particle swarm optimization (PSO) and grey wolf optimization (GWO) in terms of convergence velocity, tracking precision, and the reduction in iteration power oscillation magnitude. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we mainly study the effective dynamic behavior of a class of stochastic parabolic equations driven by Lévy noise with a fast oscillation, and the coefficients of the system are assumed to satisfy the non‐Lipschitz condition. The work in the article is roughly divided into two parts. The first part, due to the change of conditions, we must consider the existence and uniqueness of the solution of the system. In the second part, we show that the original system driven by Lévy noise is reduced into an effective equation. To be more accurate, the fast component equation is averaged out, and there exists an effective process converging to the original stochastic parabolic equation. The main contribution is that the obtained results can extend the existing results from the Lipschitz condition to a weaker condition with a wider application scope, that is, the non‐Lipschitz condition, and the driving process is Lévy noise, which seems new in the existing literature. [ABSTRACT FROM AUTHOR]

To address the issues of poor population diversity, low accuracy, and susceptibility to local optima in the Butterfly Optimization Algorithm (BOA), an Improved Butterfly Optimization Algorithm with multiple strategies (IBOA) is proposed. The algorithm employs SPM mapping and reverse learning methods to initialize the population, enhancing its diversity; utilizes Lévy flight and trigonometric search strategies to update individual positions during global and local search phases, respectively, expanding the search scope of the algorithm and preventing it from falling into local optima; and finally, it introduces a simulated annealing mechanism to accept worse solutions with a certain probability, enriching the diversity of solutions during the optimization process. Simulation experimental results comparing the IBOA with Particle Swarm Optimization, BOA, and three other improved BOA algorithms on ten benchmark functions demonstrate that the IBOA has improved convergence speed and search accuracy. [ABSTRACT FROM AUTHOR]

Malaria remains a critical public health challenge in Africa, demanding innovative control strategies. This study introduces a novel approach using Microsporidia MB -infected mosquitoes and stochastic optimal control within a Lévy process framework to regulate mosquito release strategies. The primary goal is to optimize Microsporidia MB prevalence within mosquito populations to disrupt Plasmodium transmission to humans. By incorporating Lévy noise into the modeling process, we capture the inherent randomness of mosquito dynamics, improving intervention accuracy. The model, guided by the Hamilton–Jacobi–Bellman (HJB) equation, optimizes release protocols while accounting for key environmental factors like seasonality and temperature fluctuations. Results show that intervention success depends on local climatic conditions, underscoring the need for flexible, region-specific strategies in malaria-endemic areas. Focus regions include Kenya, Ghana, Niger, and Benin, where Microsporidia MB has been confirmed. Findings suggest that targeted mosquito releases could significantly reduce malaria transmission, offering valuable insights for public health efforts. [ABSTRACT FROM AUTHOR]

An approximate algorithm for calculating integral convolution operators that arise when estimating barrier options in Lévy models using the Wiener–Hopf method is constructed. Additionally, the possibility of applying machine learning methods (artificial neural networks) to approximating a special type of integrals, which are a key element in the construction of approximate formulas for the considered Wiener–Hopf integral operators, is studied. The main idea is to expand the price function in the Fourier series and transform the integration contour for each term of the Fourier series. As a result, we obtain a set of typical integrals that depend on the Wiener–Hopf factors but are independent of the price function; then, the most computationally expensive part of the numerical method is reduced to calculating these integrals. Since they only need to be calculated once, rather than at each iteration as was the case in standard implementations of the Wiener–Hopf method, this will significantly speed up the calculations. Moreover, a neural network can be trained to calculate typical integrals. The proposed approach is especially efficient for spectrally one-sided Lévy processes for which explicit Wiener–Hopf factorization formulas are known. In this case, we obtain formulas convenient for calculations by integrating along the cut. The main advantage of including neural networks in the computational scheme is the ability to perform calculations on a nonuniform grid. Such a hybrid numerical method can successfully compete with classical methods for calculating convolutions in similar problems using the fast Fourier transform. Computational experiments show that neural networks with one hidden layer of 20 neurons are able to efficiently cope with the problems of approximating the auxiliary integrals under consideration. [ABSTRACT FROM AUTHOR]

With the growing popularity of the regime-switching Lévy processes model in option pricing, the coupled tempered fractional diffusion equation generated from this process has garnered considerable attention. However, solving this equation is challenging due to its coupling with a Markov generator matrix, which prevents the coefficient matrix derived from the fully implicit scheme from having a Toeplitz-like structure. Currently, there is no fast algorithm with guaranteed theoretical performance for this problem based on a fully implicit scheme. Therefore, this paper proposes a novel banded preconditioner specifically designed for the regime-switching Carr-Geman-Madan-Yor (CGMY) model. The effectiveness of the preconditioner is ensured by providing related theoretical analyses. It is shown that the eigenvalues of the preconditioned matrix cluster around one under specific parameter settings. Additionally, the condition number of the preconditioned matrix is bounded by a constant without any specific parameter requirements. The proposed preconditioner and theoretical analyses can be extended to the regime-switching CGMYe model as well. Finally, the accuracy of the considered models and the effectiveness of the proposed banded preconditioner are demonstrated through three numerical examples, including an empirical example. [ABSTRACT FROM AUTHOR]

This paper proposes an Improved Spider Wasp Optimizer (ISWO) to address inaccuracies in calculating the population (N) during iterations of the SWO algorithm. By innovating the population iteration formula and integrating the advantages of Differential Evolution and the Crayfish Optimization Algorithm, along with introducing an opposition-based learning strategy, ISWO accelerates convergence. The adaptive parameters trade-off probability (TR) and crossover probability (Cr) are dynamically updated to balance the exploration and exploitation phases. In each generation, ISWO optimizes individual positions using Lévy flights, DE's mutation, and crossover operations, and COA's adaptive update mechanisms. The OBL strategy is applied every 10 generations to enhance population diversity. As the iterations progress, the population size gradually decreases, ultimately yielding the optimal solution and recording the convergence process. The algorithm's performance is tested using the 2017 test set, modeling a mountainous environment with a Gaussian function model. Under constraint conditions, the objective function is updated to establish a mathematical model for UAV flight. The minimal cost for obstacle-avoiding flight within the specified airspace is obtained using the fitness function, and the flight path is smoothed through cubic spline interpolation. Overall, ISWO generates high-quality, smooth paths with fewer iterations, overcoming premature convergence and the insufficient local search capabilities of traditional genetic algorithms, adapting to complex terrains, and providing an efficient and reliable solution. [ABSTRACT FROM AUTHOR]

In this work we present an easy and direct construction of a Stochastic integral respect a cylindrical martingale-Lévy process. To do this, we apply the radonification technique. The radonification technique has been very useful to define an genuine stochastic process starting from a cylindrical process combine with Hilbert–Schmidt operators. With this work we present a self-contained construction, easy to follow to understand this new integration theories that are getting strong nowadays. [ABSTRACT FROM AUTHOR]

This paper presents a novel optimization algorithm called hyper-heuristic fitness-distance balance success-history-based adaptive differential evolution (HH-FDB-SHADE). The hyper-heuristic algorithms have two main structures: a hyper-selection framework and a low-level heuristic (LLH) pool. In the proposed algorithm, the FDB method is preferred as a high-level selection framework to evaluate the LLH pool algorithms. In addition, a total of 10 different strategies is derived from five mutation operators and two crossover methods for using them as the LLH pool. Balancing the exploration and exploitation capability of FDB is the main reason for being the selection framework of the proposed algorithm. The success of the HH-FDB-SHADE algorithm was tested on CEC-17 and CEC-20 benchmark test suits for different dimensional search spaces, and the obtained solutions from the HH-FDB-SHADE were compared to 10 different LLH pool algorithms. In addition, the HH-FDB-SHADE algorithm has been applied to optimize the control parameters of PID, PIDF, FOPID, and PIDD2 in the optimal automatic voltage regulator (AVR) design problem to reveal the improved algorithm's performance more clearly and prove its success in solving engineering problems. The results obtained from the AVR system are compared with five other effective meta-heuristic search algorithms such as the fitness-distance balance Lévy Flight distribution, differential evolution, Harris–Hawks optimization, Barnacles mating optimizer, and Moth–Flame optimization algorithms in the literature. The results of the statistical analyses indicate that HH-FDB-SHADE is the best-ranked algorithm for solving CEC-17 and CEC-20 benchmark problems and gives better results compared to the LLH pool algorithms. Besides, the proposed algorithm is more effective and robust than five other meta-heuristic algorithms in solving optimal AVR design problems. [ABSTRACT FROM AUTHOR]

The paper considers a nonstandard risk model with stochastic return and perturbation, in which the price process of the investment portfolio is described as a geometric Lévy process and each main claim may induce a delayed by-claim. When the main claims and by-claims have subexponential distributions, we obtain some asymptotic estimations of the finite-time ruin probability. [ABSTRACT FROM AUTHOR]

Long short-term memory (LSTM) networks, widely used for financial time series forecasting, face challenges in arbitrage spread prediction, especially in hyperparameter tuning for large datasets. These issues affect model complexity and adaptability to market dynamics. Existing heuristic algorithms for LSTM often struggle to capture the complex dynamics of futures spread data, limiting prediction accuracy. We propose an integrated Cuckoo and Zebra Algorithms-optimised LSTM (ICS-LSTM) network for arbitrage spread prediction. This method replaces the Lévy flight in the Cuckoo algorithm with the Zebra algorithm search, improving convergence speed and solution optimization. Experimental results showed a mean absolute percentage error (MAPE) of 0.011, mean square error (MSE) of 3.326, mean absolute error (MAE) of 1.267, and coefficient of determination (R2) of 0.996. The proposed model improved performance by reducing MAPE by 8.3–50.0%, MSE by 10.2–77.8%, and MAE by 9.3–63.0% compared to existing methods. These improvements translate to more accurate spread predictions, enhancing arbitrage opportunities and trading strategy profitability. [ABSTRACT FROM AUTHOR]

Lévy processes with increasing sample paths or subordinators are widely used in Operations Research and Engineering. The main areas of applications of these stochastic processes are insurance mathematics, inventory control, maintenance and reliability theory. Special and well-known instances of these increasing processes are stationary Poisson and compound Poisson processes. Since increasing Lévy processes are mostly regarded as special instances of continuous time martingales the main properties of Lévy processes are derived by applying general results available for martingales. However, understanding the theory of martingales requires a deep insight into the theory of stochastic processes and so it might be difficult to understand the proofs of the main properties of increasing Lévy processes. Therefore, the main purpose of this study is to relate increasing Lévy processes to simpler stochastic processes and give simpler proofs of the main properties. Fortunately, there is a natural way linking increasing Lévy processes to random processes occurring within renewal theory. Using this (sample path) approach and applying properties of random processes occurring within renewal theory we are able to analyze the undershoot and overshoot random process of an increasing Lévy process. Next to well-known results we also derive new results in this paper. In particular, we extend Lorden’s inequality for the renewal function and the residual life process to the expected overshoot of an increasing Lévy process at level r. [ABSTRACT FROM AUTHOR]

In Intelligent Manufacturing, Big Data and industrial information enable enterprises to closely monitor and respond to precise changes in both internal processes and external environmental factors, ensuring more informed decision-making and adaptive system management. It also promotes decision making and provides scientific analysis to enhance the efficiency of the operation, cost reduction, maximizing the process of production and so on. Various methods are employed to enhance productivity, yet achieving sustainable manufacturing remains a complex challenge that requires careful consideration. This study aims to develop a methodology for effective manufacturing sustainability by proposing a novel Hybrid Weighted Support Vector-based Lévy flight (HWS-LF) algorithm. The objective of the HWS-LF method is to improve the environmental, economic, and social aspects of manufacturing processes. In this approach, Support Vector Machines (SVM) are used to classify data points by identifying the optimal hyperplane to separate different classes, thereby supporting predictive maintenance and quality control in manufacturing. Random Forest is applied to boost efficiency, resource allocation, and production optimization. A Weighted Average Ensemble technique is employed to combine predictions from multiple models, assigning different weights to ensure an accurate system for evaluating manufacturing performance. Additionally, Lévy flight Optimization is incorporated to enhance the performance of the HWS-LF method further. The method's effectiveness is assessed using various evaluation metrics, including accuracy, precision, recall, F1-score, and specificity. Results show that the proposed HWS-LF method outperforms other state-of-the-art techniques, demonstrating superior productivity and system performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal time-consistent investment and reinsurance strategies for mean-variance insurers with a general Lévy Process model. Expressly, the insurers are allowed to purchase proportional reinsurance and invest in a financial market, where the surplus of the insurers is assumed to follow a Cramér–Lundberg model and the financial market consists of one risk-free asset and one risky asset whose price process is driven by a general Lévy process. Through the verification theorem, the closed-form expressions of the optimal strategies under the mean-variance criterion are derived by a complex partial integral differential Hamilton–Jacobi–Bellman equations. Finally, numerical simulations are provided to verify the effectiveness of the proposed optimal strategies and some economic interpretations are drawn. [ABSTRACT FROM AUTHOR]

We consider the problem of obtaining effective representations for the solutions of linear, vector-valued stochastic differential equations (SDEs) driven by non-Gaussian pure-jump Lévy processes, and we show how such representations lead to efficient simulation methods. The processes considered constitute a broad class of models that find application across the physical and biological sciences, mathematics, finance, and engineering. Motivated by important relevant problems in statistical inference, we derive new, generalised shot-noise simulation methods whenever a normal variance-mean (NVM) mixture representation exists for the driving Lévy process, including the generalised hyperbolic, normal-gamma, and normal tempered stable cases. Simple, explicit conditions are identified for the convergence of the residual of a truncated shot-noise representation to a Brownian motion in the case of the pure Lévy process, and to a Brownian-driven SDE in the case of the Lévy-driven SDE. These results provide Gaussian approximations to the small jumps of the process under the NVM representation. The resulting representations are of particular importance in state inference and parameter estimation for Lévy-driven SDE models, since the resulting conditionally Gaussian structures can be readily incorporated into latent variable inference methods such as Markov chain Monte Carlo, expectation-maximisation, and sequential Monte Carlo. [ABSTRACT FROM AUTHOR]

In order to address the issue of automatic charging for electric vehicles, a hanging automatic charging system was proposed, with a particular focus on the time-optimal trajectory planning of the robotic arm within the system. Additionally, a multi-strategy improved Sand Cat Swarm Optimization Algorithm (YSCSO) was put forth as a potential solution. The 0805A six-axis manipulator was selected as the research object, and a kinematic model was constructed using the D-H parameter method. The 5-7-5 polynomial interpolation function was proposed and solved to construct the motion trajectory of the robotic arm joint. The cubic chaos-refraction inverse learning, introduced to initialize the population based on the sand cat swarm algorithm SCSO, balances the relationship between the elite pool weighted guided search behavior and the spiral Lévy flight predation behavior through the use of a dynamic nonlinear sensitivity range. Furthermore, the vigilance behavior mechanism of the sand cat was increased to improve the overall optimization performance of the algorithm. The proposed method was applied to 36 benchmark functions of global optimization, and the improvement strategy, convergence behavior, population diversity, exploration, and development of the algorithm were experimentally analyzed. The results demonstrated that the proposed method exhibited superior performance, with 80.86% of the test results significantly different from those of the comparison algorithm. Three constrained mechanical design optimization problems were employed to assess the algorithm's practicality in engineering applications. Subsequently, the algorithm was applied to the optimal trajectory planning of a robotic arm, resulting in a significant reduction in the optimized joint motion time, a smooth and continuous kinematic curve devoid of abrupt changes, and a 42.72% reduction in motion time. These findings further substantiate the theoretical feasibility and superiority of the algorithm in addressing engineering challenges. [ABSTRACT FROM AUTHOR]

The dynamic and multimodal nature of photovoltaic (PV) systems makes it challenging to examine all solar photovoltaic characteristics. Consequently, this study recommends a recently developed optimization method called the marine predator algorithm (MPA) for developing reliable PV models. In the traditional MPA, the two main search processes are Lévy flight (LF) and Brownian walk (BW), and the switch across them is unpredictable. This is while the transition between these two mechanisms is naturally continuous and dynamic. To rectify the limitation mentioned above, this research paper presents an innovative, dynamic shift function that effectively modulates the interplay that exists between the BW and LF procedures. By enhancing the changeover pattern between the primary phases of MPA, the suggested dynamic walk substantially boosts the performance of MPA. The dynamic Lévy-Brownian MPA (DLBMPA) is also made to be resilient in dealing with the parameterization limitations of PV Modeling approaches by using a constraint handling technique. The performance of DLBMPA is tested using ten popular optimization methods. Employing the DLBMPA achieved an average RMSE of 9.7 × 10− 4 in the parameter estimation across a number of multiple PV models, including the SDM, DDM, and TDM, where out of the ten optimization algorithms experimented, this was statistically significant (p < 0.05) better. In terms of averaged computation time, DLBMPA was 13 ms and still showed high accuracy in dealing with different irradiance and temperature levels. These improvements allow for MBPA to be credited as having a high efficiency when estimating the PV parameters since its speed of convergence and accuracy level surpass the previous techniques used. [ABSTRACT FROM AUTHOR]

Understanding the navigation through semi-dense crowds at intersections poses a significant challenge in pedestrian dynamics, with implications for facility design and insights into emergent collective behavior. To tackle this problem, a system of cognitive active agents at a crowded three-way intersection is studied using Langevin simulations of intelligent active Brownian particles (iABPs) with directed visual perception (resulting in non-reciprocal interactions) and self-steering avoidance—without volume exclusion. We find that the emergent self-organization depends on agent maneuverability, goal fixation, and vision angle, and identify several forms of collective behavior, including localized flocking, jamming and percolation, and self-organized rotational flows. Additionally, we demonstrate that the motion of individual agents can be characterized by fractional Brownian motion and Lévy walk models across different parameter regimes. Moreover, despite the rich variety of collective behavior, the fundamental flow diagram shows a universal curve for different vision angles. Our research highlights the impact of collision avoidance, goal following, and vision angle on the individual and collective dynamics of interacting pedestrians. The study of self-organisation of pedestrian movement at crossing is important for the design of strategies facilitating pedestrian flow in crowded areas and the mitigation of crowd-related accidents. The authors study the motion of pedestrians using a model inspired from active matter systems finding interesting phases of three interacting streams of agents, including jamming, and the emergence of a vortex state. [ABSTRACT FROM AUTHOR]

To address the path planning problem for unmanned combat aerial vehicle (UCAV) more effectively, a novel two-stage path planning model is proposed. The first stage involves a longitudinal search primarily aimed at predicting the initial path, while the second stage is a horizontal search designed to correct the initial path. Furthermore, to tackle the UCAV path planning issue more effectively, this paper designs an improved elephant clan optimization (IECO) algorithm based on the average sample learning strategy, opposition-based learning, and Lévy flight disturbance strategy. Subsequently, IECO is integrated with the two-stage model (TSIECO) to address the UCAV path planning problem. Additionally, numerical experiments across 15 test functions reveal that IECO outperforms other algorithms in terms of optimization capability and convergence speed. Finally, the UCAV path planning experimental results indicate that the two-stage model based on IECO, as proposed in this paper, has significant advantages over traditional path planning models based on other swarm intelligence algorithms. Specifically, in three different simulated environments, the TSIECO has been tested on a total of 9 maps with varying parameters, yielding paths that are optimal in terms of cost and stability. [ABSTRACT FROM AUTHOR]

Non-fungible tokens (NFTs), which are immutable and transferable tokens on blockchain networks, have been used to certify the ownership of digital images often grouped in collections. Depending on individual interests, wallets explore and purchase NFTs in one or more image collections. Among many potential factors of shaping purchase trajectories, this paper specifically examines how visual similarities between collections affect wallets' explorations. Our model characterizes each wallet's explorations with a Lévy flight and shows that wallets tend to favor collections having similar visual features to their previous purchases while their behaviors vary widely. The model also predicts the extent to which the next collection is close to the most recent collection of purchases with respect to visual features. These results are expected to enhance and support recommendation systems for the NFT market. [ABSTRACT FROM AUTHOR]

In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative Lévy processes using the binomial expansion approach. More specifically, we study the distributions of such excursions and related quantities such as the joint distribution of the shortest and longest negative excursions and their difference (also known as the range) over a random and infinite horizon time. Our results are applied to address new Parisian ruin problems, stochastic ordering and the number near-maximum distress periods showing the superiority of the binomial expansion approach for such cases. [ABSTRACT FROM AUTHOR]

With advancements in integrated space–air–ground global observation capabilities, the volume of remote sensing data is experiencing exponential growth. Traditional computing models can no longer meet the task processing demands brought about by the vast amounts of remote sensing data. As an important means of processing remote sensing data, distributed cluster computing's task scheduling directly impacts the completion time and the efficiency of computing resource utilization. To enhance task processing efficiency and optimize the allocation of computing resources, this study proposes a Multi-Strategy Improved Siberian Tiger Optimization (MSSTO) algorithm based on the original Siberian Tiger Optimization (STO) algorithm. The MSSTO algorithm integrates the Tent chaotic map, the Lévy flight strategy, Cauchy mutation, and a learning strategy, showing significant advantages in convergence speed and global optimal solution search compared to the STO algorithm. By combining stochastic key encoding schemes and uniform allocation encoding schemes, taking the task scheduling of aerosol optical depth retrieval as a case study, the research results show that the MSSTO algorithm significantly shortens the completion time (21% shorter compared to the original STO algorithm and an average of 15% shorter compared to nine advanced algorithms, such as a particle swarm algorithm and a gray wolf algorithm). It demonstrates superior solution accuracy and convergence speed over various competing algorithms, achieving the optimal execution sequence and machine allocation scheme for task scheduling. [ABSTRACT FROM AUTHOR]

The Zebra Optimization Algorithm (ZOA) mimics the social behavior of zebras and is susceptible to the interference of local optimal solutions, leading to poor optimization and premature convergence. In this paper, we propose an improved zebra optimization algorithm (IZOA) that integrates several advanced strategies to overcome these problems. First, IZOA introduces a Lévy flight strategy in the foraging phase of the zebra population to expand the search range and improve the quality of individuals. At the same time, the "PZ" mechanism updates the other individuals based on the value of the leading zebra in each generation, which accelerates the optimization process and improves the searching ability. In addition, IZOA integrates a nonlinear convergence factor based on the COS function, which improves the convergence speed and balances the exploration and development phases. A Cauchy variation strategy is used to enhance the global search capability and help the population escape from local extremes. In CEC2017 and CEC2022 benchmarking and rolling bearing design applications, IZOA is compared with 12 mainstream and improved ZOA algorithms (CZOA and IIZOA), and shows better performance. Finally, IZOA is combined with LSTM network for wind power prediction to show its application advantages in real engineering design problems. [ABSTRACT FROM AUTHOR]

The Wiener–Hopf factorisation of a Lévy or Markov additive process describes the way that it attains new extrema in terms of a pair of so-called ladder height processes. Vigon's theory of friendship for Lévy processes addresses the inverse problem: when does a process exist which has certain prescribed ladder height processes? We give a complete answer to this problem for Markov additive processes, provide simpler sufficient conditions for constructing processes using friendship, and address in part the question of the uniqueness of the Wiener–Hopf factorisation for Markov additive processes. [ABSTRACT FROM AUTHOR]

In this article, we show the existence of a universal Skorohod measurable functional representation for a large class of semimartingale-driven stochastic differential equations. For this, we prove that paths of the strong solutions of stochastic differential equations can be written as measurable functions of the paths of their driving processes into the space of all càdlàg functions equipped with the Borel sigma-field generated by all open sets with respect to the Skorohod metric. This result can be applied to calculate Malliavin derivatives for SDEs driven by pure-jump Lévy processes with drift. [ABSTRACT FROM AUTHOR]

Inspired by the work of Lkabous (2021), we consider Poissonian occupation times below level 0 of a refracted Lévy process where its premium rate is adaptive. In this model, occupation time is accumulated once the surplus process is observed to be negative at Poisson arrival times. Our analysis depends on various exit identities for refracted Lévy processes observed at Poisson arrival times. As an application of Poissonian occupation times, we derive an explicit expression for the probability of Parisian ruin with Erlang(2, λ) implementation delays. The resulting main quantities are in terms of scale functions. [ABSTRACT FROM AUTHOR]

In the edge computing environment of smart buildings, to minimize the overall system latency and energy consumption in resource-constrained and complex conditions, this paper proposed an edge computing offloading method based on data compression and improved gray wolf algorithm (CLGWO). Firstly, it used the differential dictionary encoding compression method to estimate the data compression rate and the overhead incurred by compression. It combined the Lévy flight algorithm and spiral asymptotic hunting method to enhance the global search capability of the grey wolf optimizer. Finally, it determined the optimal offloading scheme by combining the estimated compression effects with the improved grey wolf optimizer. Experimental results indicate that the CLGWO method reduces the overall latency and energy consumption of computing task offloading, thereby verifying its effectiveness and feasibility. This approach provides a new solution to the edge computing offloading problem in buildings. [ABSTRACT FROM AUTHOR]

Coverage control is a fundamental and critical issue in plentiful wireless sensor network (WSN) applications. Aiming at the high-dimensional optimization problem of sensor node deployment and the complexity of the monitoring area, an orthogonal learning multi-strategy bald eagle search (OLMBES) algorithm is proposed to optimize the location deployment of sensor nodes. This paper incorporates three kinds of strategies into the bald eagle search (BES) algorithm, including Lévy flight, quasi-reflection-based learning, and quadratic interpolation, which enhances the global exploration ability of the algorithm and accelerates the convergence speed. Furthermore, orthogonal learning is integrated into BES to improve the algorithm's robustness and premature convergence problem. By this way, population search information is fully utilized to generate a more superior position guidance vector, which helps the algorithm jump out of the local optimal solution. Simulation results on CEC2014 benchmark functions reveal that the optimization performance of the proposed approach is better than that of the existing method. On the WSN coverage optimization problem, the proposed method has greater network coverage ratio, node uniformity, and stronger optimization stability when compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Feasible, smooth, and time-jerk optimal trajectory is essential for manipulators utilized in manufacturing process. A novel technique to generate trajectories in the joint space for robotic manipulators based on quintic B-spline and constrained multi-objective student psychology based optimization (CMOSPBO) is proposed in this paper. In order to obtain the optimal trajectories, two objective functions including the total travelling time and the integral of the squared jerk along the whole trajectories are considered. The whole trajectories are interpolated by quintic B-spline and then optimized by CMOSPBO, while taking into account kinematic constraints of velocity, acceleration, and jerk. CMOSPBO mainly includes improved student psychology based optimization, archive management, and an adaptive ε-constraint handling method. Lévy flights and differential mutation are adopted to enhance the global exploration capacity of the improved SPBO. The ε value is varied with iterations and feasible solutions to prevent the premature convergence of CMOSPBO. Solution density estimation corresponding to the solution distribution in decision space and objective space is proposed to increase the diversity of solutions. The experimental results show that CMOSPBO outperforms than SQP, and NSGA-II in terms of the motion efficiency and jerk. The comparison results demonstrate the effectiveness of the proposed method to generate time-jerk optimal and jerk-continuous trajectories for manipulators. [ABSTRACT FROM AUTHOR]

The growth optimizer (GO) is an innovative and robust metaheuristic optimization algorithm designed to simulate the learning and reflective processes experienced by individuals as they mature within the social environment. However, the original GO algorithm is constrained by two significant limitations: slow convergence and high memory requirements. This restricts its application to large-scale and complex problems. To address these problems, this paper proposes an innovative enhanced growth optimizer (eGO). In contrast to conventional population-based optimization algorithms, the eGO algorithm utilizes a probabilistic model, designated as the virtual population, which is capable of accurately replicating the behavior of actual populations while simultaneously reducing memory consumption. Furthermore, this paper introduces the Lévy flight mechanism, which enhances the diversity and flexibility of the search process, thus further improving the algorithm's global search capability and convergence speed. To verify the effectiveness of the eGO algorithm, a series of experiments were conducted using the CEC2014 and CEC2017 test sets. The results demonstrate that the eGO algorithm outperforms the original GO algorithm and other compact algorithms regarding memory usage and convergence speed, thus exhibiting powerful optimization capabilities. Finally, the eGO algorithm was applied to image fusion. Through a comparative analysis with the existing PSO and GO algorithms and other compact algorithms, the eGO algorithm demonstrates superior performance in image fusion. [ABSTRACT FROM AUTHOR]

Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a Lévy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In order to do so, we study the law of this family of processes in the infinite mean case and provide necessary and sufficient conditions for the process to be conservative, i.e. that the process does not explode in finite time a.s. In addition, we establish precise rates for the non-explosion probabilities in the subcritical and critical regimes, first found by Palau et al. (ALEA Lat Am J Probab Math Stat 13(2):1235–1258, 2016) in the case when the branching mechanism is given by the negative of the Laplace exponent of a stable subordinator. [ABSTRACT FROM AUTHOR]

In this article, we derive (local) orthogonality graphs for the popular continuous‐time state space models, including in particular multivariate continuous‐time ARMA (MCARMA) processes. In these (local) orthogonality graphs, vertices represent the components of the process, directed edges between the vertices indicate causal influences and undirected edges indicate contemporaneous correlations between the component processes. We present sufficient criteria for state space models to satisfy the assumptions of Fasen‐Hartmann and Schenk (2024a) so that the (local) orthogonality graphs are well‐defined and various Markov properties hold. Both directed and undirected edges in these graphs are characterised by orthogonal projections on well‐defined linear spaces. To compute these orthogonal projections, we use the unique controller canonical form of a state space model, which exists under mild assumptions, to recover the input process from the output process. We are then able to derive some alternative representations of the output process and its highest derivative. Finally, we apply these representations to calculate the necessary orthogonal projections, which culminate in the characterisations of the edges in the (local) orthogonality graph. These characterisations are given by the parameters of the controller canonical form and the covariance matrix of the driving Lévy process. [ABSTRACT FROM AUTHOR]

U‐shaped automated container terminals (ACTs) represent a strategic design in port infrastructure that facilitates simultaneous loading and unloading operations. This paper addresses the challenges of scheduling multiple types of equipment, such as dual trolley quay cranes (DTQCs), automated guided vehicles (AGVs), double cantilever rail cranes (DCRCs), and external trucks (ETs) in U‐shaped ACTs. This paper proposes a mixed integer linear programming model for optimizing the multiple equipment scheduling, aiming to minimize container completion time and AGV waiting time simultaneously. This paper customizes a hybrid genetic‐cuckoo optimization algorithm (HGCOA) with double‐point crossover and Lévy flight Cuckoo search strategies. Extensive numerical results show that the proposed HGCOA outperforms the benchmark genetic algorithms in terms of solution quality and computational time while significantly improving efficiency without substantial sacrifices in solution quality compared with the exact solution method. Overall, this study presents a promising solution for enhancing coordination and operation efficiency in U‐shaped ACTs. [ABSTRACT FROM AUTHOR]