Qualitative behaviour of solutions of stochastic reaction-diffusion equations

AbstractWe consider semilinear stochastic evolution equations driven by a cylindrical Wiener process. They can be used as models for stochastic reaction-diffusion systems. Under certain conditions we prove existence, uniqueness and ergodicity of the invariant measure and the strong law of large numbers. For this purpose a Girsanov type theorem is also proved. These results are applied to stochastic-reaction diffusion equations appearing in physics