Abstract
We present the Girsanov theorem for a non linear Ito equation in an infinite dimensional Hilbert space with a non linearity of polynomial growth and an infinite dimensional additive noise. We assume a condition weaker than Novikov one, as done by Mikulevicius and Rozovskii in the study of more general stochastic PDE's. The equivalence of the laws of the linear equation and of the non linear equation implies results on weak solutions and on invariant measures for the given non linear equation. Two examples are presented: a stochastic Kuramoto-Sivashinsky equation and a stochastic hyperviscosity-regularized Navier-Stokes equation.
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