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

Leonid Mytnik·Edwin Perkins·Anja Sturm
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Abstract

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.

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Leonid Mytnik, Edwin Perkins, Anja Sturm. 2005-07-26. On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients. https://arxiv.org/abs/math/0507545

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