Acta mathematica scientia, Series B >
EXPONENTIAL STABILITY FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION
Received date: 2012-05-28
Revised date: 2013-08-15
Online published: 2014-07-20
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)
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.
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 . DOI: 10.1016/S0252-9602(14)60083-7
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