Stochastic generalized porous media and fast diffusion equations

We present a generalization of Krylov-Rozovskii’s result on the existence and unique-ness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for σ-finite reference measures, where the drift term is given by a negative definite operator acting on a time-dependent function, which belongs to a large class of functions comparable with the so-called N-functions in the theory of Orlicz spaces. AMS subject Classification: 76S05, 60H15