Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises

Xiao Wang, Jinqiao Duan, Xiaofan Li and Yuanchao Luan

Applied Mathematics and Computation, 2015, vol. 258, issue C, 282-295

Abstract: The mean exit time and escape probability are deterministic quantities that can quantify dynamical behaviors of stochastic differential equations with non-Gaussian α-stable type Lévy motions. Both deterministic quantities are characterized by differential–integral equations (i.e., differential equations with nonlocal terms) but with different exterior conditions. A convergent numerical scheme is developed and validated for computing the mean exit time and escape probability for two-dimensional stochastic systems with rotationally symmetric α-stable type Lévy motions. The effects of drift, Gaussian noises, intensity of jump measure and domain sizes on the mean exit time are discussed. The difference between the one-dimensional and two-dimensional cases is also presented.

Keywords: Stochastic dynamical systems; Lévy motion; Differential–integral equation; First exit time; Escape probability (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:258:y:2015:i:c:p:282-295

DOI: 10.1016/j.amc.2015.01.117

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