I'm fairly familiar with the literature dealing with convergence of SDEs in $\mathbb{R}^d$ but recently I've needed to use extended results dealing with convergence of SDEs in Hilbert Spaces. However I am quite unfamiliar with the subject.

My question what is a good *reference* treating the following question:

If $W(t)$ is a cylindrical (or Q-)Wiener process with values in a Hilbert space H and $\mu_n$ as well as $\Sigma_n$ are a sequence of adapted to the filtration generated by $W(t)$ then under what circumstances does the solution to the SDEs $$ dX_n(t) = \mu_n(t,X_n(t))dt +\sigma_n(t,X_n(t))dW(t) $$ converge to the solution of the SDE $$ dX(t) = \lim_{n\mapsto \infty}\mu_n(t,X_n(t))dt +\lim_{n\mapsto \infty}\sigma_n(t,X_n(t))dW(t)? $$