The exponential stability  of nonlinear stochastic differential systems whose coefficients obey the polynomial growth polynomial growth

Liu Lei; Shen Yi; Sun Peng

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The exponential stability of nonlinear stochastic differential systems whose coefficients obey the polynomial growth polynomial growth

Liu Lei #,Shen Yi *,Sun Peng

Department of Control Science and Engineering, Huazhong University of Science and Technology

*Correspondence author

#Submitted by

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Funding: The project reported here is supported by the Specialized Research Fund for the Doctoral Program of HigherEducation of China. （No.Grant No.20070487052）

Opened online:30 June 2010

Accepted by: none

Citation: Liu Lei ,Shen Yi ,Sun Peng .The exponential stability of nonlinear stochastic differential systems whose coefficients obey the polynomial growth polynomial growth[OL]. [30 June 2010] http://en.paper.edu.cn/en_releasepaper/content/4377167

This paper discusses the exponential stability of nonlinear stochastic differential systems which coefficients obey the polynomial growth condition. Based on the stochastic analysis, we study the existence and uniqueness of the global solution of the nonlinear stochastic differential systems. Sufficient criteria on almost sure exponential stability and p-th moment exponential stability has been established. The new criteria is directly expressed in terms of the system coefficients and it can not only be applied much more easily but also cover a much wider class of nonlinear stochastic differential systems. The decay rate of almost sure exponential stability and p-th moment exponential stability are estimated through the system coefficients. Nontrivial examples with theirs numerical simulations are provided to illustrate our result.

Keywords:stochastic differential system;brownian motion; polynomial growth;Ito’s formula;exponential stability

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