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This note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems (SDSs). The systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition. By applying some novel techniques, some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such SDSs. We also provide the range of the order p. A numerical example is provided to illustrate the effectiveness and the benefits of the proposed result. [ABSTRACT FROM AUTHOR]

Abstract-This note studies stability problem of solutions for stochastic impulsive systems. By employing Lyapunov.like function method and Itô's formula, comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established. Based on these comparison principles, the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system. As the application, the stability results are used to design impulsive control for the stabilization of unstable stochastic systems. Finally, one example is given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]