Wong-Zakai approximations of stochastic evolution equations

Abstract.

Theorems on weak convergence of the laws of the Wong-Zakai approximations for evolution equation

$$ \begin{aligned} dX(t) & = (AX(t) + F(X(t)))dt + G(X(t))dW(t)\\ X(0) & = x \in H \end{aligned} $$

are proved. The operator A in the equation generates an analytic semigroup of linear operators on a Hilbert space H. The tightness of the approximating sequence is established using the stochastic factorisation formula. Applications to strongly damped wave and plate equations as well as to stochastic invariance are discussed.