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 - Publisher Copyright:
© 2018 Elsevier Inc.
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 -