Space-Time Regularity of Solutions of the Parabolic Stochastic Cauchy Problem

Abstract

We study space-time Hölder regularity of the solutions of the linear stochastic Cauchy problem where A is the generator of an analytic semigroup on a Banach space E and W is an E-valued Brownian motion. When −A admits a γ-bounded H ∞-calculus, the solution is shown to have maximal regularity in the sense that U has a modification with paths in . The results are applied to prove optimal and maximal Hölder space-time regularity for second-order parabolic stochastic partial differential equations.