Holder 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~${\bf R}^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large~p. We prove that the solutions are H\"older-continuous functions almost surely (a.s.)\ and that the respective H\"older norms have finite momenta of any order.