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

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.