EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

doi:10.1016/S0252-9602(14)60083-7

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1254-1270.doi: 10.1016/S0252-9602(14)60083-7

EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

周少波|薛明皋*

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China； School of Management, Huazhong University of Science and Technology, Wuhan 430074, China

收稿日期:2012-05-28 修回日期:2013-08-15 出版日期:2014-07-20 发布日期:2014-07-20
通讯作者: 薛明皋，xmgwt@mail.hust.edu.cn E-mail:hustzhshbowls@sina.com；xmgwt@mail.hust.edu.cn
基金资助:
The financial support from the National Natural Sci-ence Foundation of China (70871046, 71171091, 71191091) and Fundamental Research Funds for the Central Universities (2011QN167)

EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

ZHOU Shao-Bo, XUE Ming-Gao*

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China； School of Management, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2012-05-28 Revised:2013-08-15 Online:2014-07-20 Published:2014-07-20
Contact: XUE Ming-Gao，xmgwt@mail.hust.edu.cn E-mail:hustzhshbowls@sina.com；xmgwt@mail.hust.edu.cn
Supported by:
The financial support from the National Natural Sci-ence Foundation of China (70871046, 71171091, 71191091) and Fundamental Research Funds for the Central Universities (2011QN167)

摘要/Abstract

摘要：

The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponen-tially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.

关键词: stochastic pantograph equation, hybrid system, polynomial growth conditions, exponential stability, convergence in probability

Abstract:

Key words: stochastic pantograph equation, hybrid system, polynomial growth conditions, exponential stability, convergence in probability

中图分类号:

65C20

周少波, 薛明皋. EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION[J]. 数学物理学报(英文版), 2014, 34(4): 1254-1270.

ZHOU Shao-Bo, XUE Ming-Gao. EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION[J]. Acta mathematica scientia,Series B, 2014, 34(4): 1254-1270.

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EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

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