The solution Xn to a nonlinear stochastic differential equation of the form dXn(t)+An(t)Xn(t)dt−12∑j=1N(Bjn(t))2Xn(t)dt=∑j=1NBjn(t)Xn(t)dβjn(t)+fn(t)dt, Xn(0)=x, where βjn is a regular approximation of a Brownian motion βj, Bjn(t) is a family of linear continuous operators from V to H...

We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping.

We prove, using coupling arguments, exponential convergence to equilibrium for reaction-diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection.