Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations

2018/11/05 by Yanjie Zhang, Xiao Wang, Zhang, Yanjie +3
Economics, Econometrics and Finance · Engineering · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1811.01634

openalex publication_date 2018/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered Lévy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme to compute and solve the mean exit time associated with the one dimensional stochastic system. Secondly, we extend the analytical and numerical results to two dimensional case: horizontal-vertical and isotropic case. Finally, we verify the effectiveness of the presented schemes with numerical experiments in several examples.

Citations

• Mean Exit Time and Escape Probability for Dynamical Systems Driven by Lévy Noises

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