Pathwise Uniqueness for the Stochastic Heat Equation with Hölder Continuous Drift and Noise Coefficients

Abstract

We study the solutions of the stochastic heat equation with multiplicative space-time white noise. We prove a comparison theorem between the solutions of stochastic heat equations with the same noise coefficient which is Hölder continuous of index $\gamma >3/4$, and drift coefficients that are Lipschitz continuous. Later we use the comparison theorem to get sufficient conditions for the pathwise uniqueness for solutions of the stochastic heat equation, when both the white noise and the drift coefficients are Hölder continuous.

14 pages. arXiv admin note: text overlap with arXiv:1403.4491

References in corpus (2)

• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift
• Multiple points of the Brownian sheet in critical dimensions

Cited by in corpus (1)

• Large deviation principle for stochastic reaction-diffusion equations with super-linear drift on $\mathbb{R}$ driven by space-time white noise