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

Mytnik, Leonid; Perkins, Edwin; Sturm, Anja

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

Authors

Mytnik, Leonid

Perkins, Edwin

Sturm, Anja

Description

We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on IR^d for d greater or equal to 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 Hoelder continuity of the solutions near zero is established.
39 pages