  We provide a general framework for the stability of solutions to stochastic
partial differential equations with respect to perturbations of the drift. More
precisely, we consider stochastic partial differential equations with drift
given as the subdifferential of a convex function and prove continuous
dependence of the solutions with regard to random Mosco convergence of the
convex potentials. In particular, we identify the concept of stochastic
variational inequalities (SVI) as a well-suited framework to study such
stability properties. The generality of the developed framework is then laid
out by deducing Trotter type and homogenization results for stochastic fast
diffusion and stochastic singular p-Laplace equations. In addition, we provide
an SVI treatment for stochastic nonlocal p-Laplace equations and prove their
convergence to the respective local models.
