TY - JOUR

T1 - Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion

AU - Wang, Xiao

AU - Duan, Jinqiao

AU - Li, Xiaofan

AU - Song, Renming

N1 - Funding Information:
The research is partially supported by the grants China Scholarship Council (X.W.), National Science Foundation-DMS #1620449 (J.D. and X.L.), and Simons Foundation #429343 (R.S.).

PY - 2018/11/15

Y1 - 2018/11/15

N2 - 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.

AB - 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.

KW - Asymmetric Lévy motion

KW - Escape probability

KW - First exit time

KW - Integro-differential equation

KW - Stochastic dynamical systems

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U2 - 10.1016/j.amc.2018.05.038

DO - 10.1016/j.amc.2018.05.038

M3 - Article

AN - SCOPUS:85048874451

SN - 0096-3003

VL - 337

SP - 618

EP - 634

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -