Random attractor for damped nonlinear wave equations with white noise

We first present the existence of a random attractor of a stochastic dynamical system generated by a damped nonlinear wave equation with white noise under the Dirichlet boundary condition and estimate the explicit bound of the random attractor. And then we obtain an estimate of the upper bound of the Hausdor. dimension of the random attractor. The obtained upper bound of the Hausdor. dimension decreases as the damping grows and it is uniformly bounded if the derivative of nonlinearity is bounded; moreover, in this case, the upper bound of the Hausdor. dimension of the random attractor is just the upper bound of the Hausdor. dimension of the global attractor for the corresponding deterministic system without noise.