In this paper we first shall establish an existence and uniqueness result for the semilinear stochastic differential equations in Hilbert space dX ¼ (AX þ f(X ))dt þ g(X )dW under weaker conditions than the Lipschitz one by investigating the convergence of the successive approximations. Secondly we show, under the assumption of so-called pathwise uniqueness (PU ), the convergence of the Euler and Lie-Trotter schemes in L p , p . 2 and the continuous dependence of the solutions on the initial data and on the coefficients for such equation. Finally we study the existence of the solutions when the coefficients f and g are only defined on a subset of the state Hilbert space.

The purpose of this paper is to study the exponential stabilizability for a class of nonlinear dynamical system with a stochastic perturbation. We propose a class of continuous feedback controllers which guaranteed exponential stability of uncertain system. We close the paper by an example.

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