Pathwise uniqueness for the stochastic heat equation with Hölder continuous drift and noise coefficients

Leonid Mytnik and Eyal Neuman

Stochastic Processes and their Applications, 2015, vol. 125, issue 9, 3355-3372

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 γ>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.

Keywords: Stochastic partial differential equations; Pathwise uniqueness; White noise (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:9:p:3355-3372

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DOI: 10.1016/j.spa.2015.04.009

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