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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]

This paper considers the stabilization and destabilization by a Brownian noise perturbation that preserves the equilibrium of the ordinary differential equation x′(t) = f(x(t)). In an extension of earlier work, we lift the restriction that I obeys a global linear bound, and show that when f is locally Lipschitz, a function g can always be found so that the noise perturbation g (X (t)) dB (t) either stabilizes an unstable equilibrium, or destabilizes a stable equilibrium. When the equilibrium of the deterministic equation is nonhyperbolic, we show that a nonhyperbolic perturbation suffices to change the stability properties of the solution. [ABSTRACT FROM AUTHOR]