Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces

We study a stochastic linear evolution equation $dX+A(t)Xdt=F(t)dt+G(t)d{w}_t$ in a Banach space of M-type 2. We construct unique strict solutions to the equation on the basis of the theory of deterministic linear evolution equations. The abstract results are applied to stochastic diffusion equations.