On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

Abstract

We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on ℝ^d for d≥1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Hölder continuity of the solutions near zero is established.