The p th moment asymptotic stability and exponential stability of stochastic functional differential equations with polynomial growth condition

Advances in Difference Equations

Lichao Feng¹  Shoumei Li² 

[1] College of Applied Sciences, Beijing University of Technology, Beijing, P.R. China;College of Sciences, Hebei United University, Tangshan, P.R. China

关键词: stochastic functional differential equations;    polynomial growth condition;    p th moment asymptotic stability;    p th moment exponential stability;    almost sure exponential stability;   

DOI  :  10.1186/1687-1847-2014-302

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper mainly discusses the p th moment asymptotic stability and the exponential stability of nonlinear stochastic functional differential equations (SFDEs) satisfying the local Lipschitz condition but not the linear growth condition. These new conditions assume that the coefficients of SFDEs are polynomials or dominated by polynomials. We establish some sufficient conditions for the p th moment asymptotic stability and the exponential stability of nonlinear SFDEs by applying some novel techniques. Some nontrivial examples are provided to illustrate our results. MSC:93E03, 93D20.

【 授权许可】

CC BY