On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
Department of Mathematical Sciences
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.
Heat equation , colored noise , stochastic partial ddifferential equation , uniqueness , existence