Exponential mean square stability of numerical methods for systems of stochastic differential equations

被引:86
作者
Huang, Chengming [1 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
基金
中国国家自然科学基金;
关键词
Stochastic differential equations; Mean square stability; Exponential stability; Theta method; Poisson process; CONVERGENCE;
D O I
10.1016/j.cam.2012.03.005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is concerned with exponential mean square stability of the classical stochastic theta method and the so called split-step theta method for stochastic systems. First, we consider linear autonomous systems. Under a sufficient and necessary condition for exponential mean square stability of the exact solution, it is proved that the two classes of theta methods with theta >= 0.5 are exponentially mean square stable for all positive step sizes and the methods with theta < 0.5 are stable for some small step sizes. Then, we study the stability of the methods for nonlinear non-autonomous systems. Under a coupled condition on the drift and diffusion coefficients, it is proved that the split-step theta method with theta > 0.5 still unconditionally preserves the exponential mean square stability of the underlying systems, but the stochastic theta method does not have this property. Finally, we consider stochastic differential equations with jumps. Some similar results are derived. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码:4016 / 4026
页数:11
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