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

Xiao Wang, Jinqiao Duan, Xiaofan Li and Renming Song

Applied Mathematics and Computation, 2018, vol. 337, issue C, 618-634

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. The discretized equation has Toeplitz structure that enables utilization of fast Fourier transform in numerical simulations. 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.

Keywords: Stochastic dynamical systems; Asymmetric Lévy motion; Integro-differential equation; First exit time; Escape probability (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:618-634

DOI: 10.1016/j.amc.2018.05.038

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