A lower bound on the Hausdorff dimension of random attractors

We consider an SPDE with a Lipschitz continuous nonlinearity driven by a multiplicative noise. Its mild solution generates a random dynamical system and we discuss the existence of a random attractor. Applying a cut-off function to the nonlinearity we obtain a local unstable manifold for the random dynamical system. The local unstable manifold contains an open subset which lies also in the related random attractor. This subset is used to obtain a lower bound on the Hausdorff dimension of the random attractor.