Lyapunov exponents and stability for nonlinear SPDE's driven by finite-dimensional Wiener processes

We present new results concerning the stability properties of the global attractor associated with a class of nonlinear SPDE's driven by finite-dimensional Wiener processes of arbitrary covariance. In particular, we show how to determine explicitly certain Lyapunov exponents when the nonlinearities of the noise-terms of the equations are subordinated to the nonlinearities of the drift-terms in some sense. Our method of investigation rests upon the use of a comparison principle and of simple ergodic properties for certain Ito martingales. (C) Academie des Sciences/Elsevier, Paris.