On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
Date
2005-02-28
Authors
Mytnik, Leonid
Perkins, Edwin
Sturm, Anja
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
We consider the existence and pathwise uniqueness of the stochastic heat equation with a
multiplicative colored noise term on R
d for d greater than 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
Holder continuity of the solutions near zero is established.
Description
Keywords
Heat equation , colored noise , stochastic partial ddifferential equation , uniqueness , existence