Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: The white noise case

Abstract

We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Hölder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations. © 2009 Springer-Verlag.