Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion

2017/02/02 by Xiao Wang, Jinqiao Duan, Wang, Xiao +5
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1702.00600

openalex publication_date 2017/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent numerical method for the mean first exit time and escape probability for stochastic systems with an asymmetric Lévy motion, and analyze the properties of the solutions of the nonlocal equations. We also investigate the effects of different system factors on the mean exit time and escape probability, including the skewness parameter, the size of the domain, the drift term and the intensity of Gaussian and non-Gaussian noises. We find that the behavior of the mean exit time and the escape probability has dramatic difference at the boundary of the domain when the index of stability crosses the critical value of one.

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