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 IRd 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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