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

被引：0
作者：
Chengjian Zhang
Ying Xie
机构：
[1] Huazhong University of Science and Technology,School of Mathematics and Statistics
[2] Huazhong University of Science and Technology,Hubei Key Laboratory of Engineering Modeling and Scientific Computing
来源：
Science China Mathematics | 2019年 / 62卷
关键词：
nonlinear hybrid stochastic differential equations; time-variable delay; backward Euler-Maruyama method; strong convergence; almost surely exponential stability; 65C20; 60H35; 65L20;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：597 / 616
页数：19
相关论文
共 51 条
[1]  
Bahar A(2004)Stochastic delay Lotka-Volterra model J Math Anal Appl 292 364-380
[2]  
Mao X(2009)An analytic approximation of solutions of stochastic differential delay equations with Markovian switch-ing Math Comput Modelling 50 1379-1384
[3]  
Bao J(1996)Stability of a random diffusion with linear drift J Math Anal Appl 202 604-622
[4]  
Hou Z(2013)Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations IEEE Trans Automat Control 58 2319-2332
[5]  
Basak G K(2013)Strong predictor-corrector Euler-Maruyama methods for stochastic differential equations with Markovian switching J Comput Appl Math 237 5-17
[6]  
Bisi A(2006)Convergence and stability of numerical solutions to SDDEs with Markovian switching Appl Math Comput 175 1080-1091
[7]  
Ghosh M K(2006)Exponential stability of numerical solutions to SDDEs with Markovian switching Appl Math Comput 174 1302-1313
[8]  
Hu L(1999)Stability of stochastic differential equations with Markovian switching Stochastic Process Appl 79 45-67
[9]  
Mao X(2011)Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type condi-tions Appl Math Comput 217 5512-5524
[10]  
Zhang L(2011)Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid stochastic differential equations J Comput Appl Math 235 1213-1226
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