Stochastic evolution equations with a spatially homogeneous Wiener process

A semilinear parabolic equation on Rd with a non-additive random perturbation is studied. The noise is supposed to be a spatially homogeneous Wiener process. Conditions for the existence and uniqueness of the solution in terms of the spectral measure of the noise are given. Applications to population and geophysical models are indicated. The Freidlin-Wentzell large deviation estimates are obtained as well.