Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（3）
• 页码范围: 597-616
• 页数: 20页
• 语种: 英文

摘要

In this paper,we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay.Under the local Lipschitz condition and polynomial growth condition,it is proved that the backward Euler-Maruyama method is strongly convergent.Additionally,the moment estimates and almost sure exponential stability for the analytical solution are proved.Also,under the appropriate condition,we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable.A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.