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

被引：19
作者：
Wang, Xiao [1 ,2 ]
Duan, Jinqiao [2 ]
Li, Xiaofan [2 ]
Luan, Yuanchao [2 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] IIT, Dept Appl Math, Chicago, IL 60616 USA
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 258卷
关键词：
Stochastic dynamical systems; Levy motion; Differential-integral equation; First exit time; Escape probability; LEVY PROCESSES; DRIVEN;
D O I：
10.1016/j.amc.2015.01.117
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The mean exit time and escape probability are deterministic quantities that can quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy 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 alpha-stable type Levy 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. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：282 / 295
页数：14
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