相关论文: A maximum likelihood estimation of L\'evy-driven s…

With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of…

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…

Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and…

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…

Trust is the invisible glue that holds together the fabric of societies, economic systems, and political institutions. Yet, its dynamics-especially in real-world settings remain unpredictable and difficult to control. While classical trust…

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

In a high-frequency context, we investigate the efficient estimation of scaling and jump activity parameters for a stochastic differential equation driven by a L{\'e}vy process with both diffusion component and pure-jump component. We first…

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental…

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian…

We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…

This paper enhances the classical Solow model of economic growth by integrating L\'evy noise, a type of non-Gaussian stochastic perturbation, to capture the inherent uncertainties in economic systems. The extended model examines the impact…

Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of L\'evy…

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 L\'evy processes, and we show how such representations lead…

Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically…

Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random…