An approach to Ito linear equations in Hilbert spaces by approximation of white noise with coloured noise

We consider the stochastic problem , in a Hilbert space H, where f,X are prescribed data, Wt is a real Brownian motion, and A(t), B generate an analytic semi-group and a strongly continuous group respectively. The domains D(A (t)) may vary with t and we only require D(A(t))CD(B) for each t. A unique generalized solution is constructed as the pathwise uniform limit of solutions of suitable approximating deterministic problems, which are obtained by approaching the white noise dWt with a sequence of regular coloured noises