H\"older 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 H\"older-continuous functions almost surely (a.s.) and that the respective H\"older norms have finite momenta of any order.