Hölder estimates for solutions of parabolic SPDEs

Abstract

This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of ${\mathbb{R}}^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large $p$. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective Hölder norms have finite momenta of any order.