Schauder estimates for stationary and evolution equations associated to stochastic reaction-diffusion equations driven by colored noise

Abstract

We consider stochastic reaction-diffusion equations with colored noise on the space of real-valued and continuous functions on a compact subset of ℝ d for d = 1 , 2 , 3 . We prove Schauder-type estimates, which will depend on the color of the noise, for the stationary and evolution problems associated with the corresponding transition semigroup.