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

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  • Mytnik, Leonid
  • Neuman, Eyal

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.

Suggested Citation

  • Mytnik, Leonid & Neuman, Eyal, 2015. "Pathwise uniqueness for the stochastic heat equation with Hölder continuous drift and noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3355-3372.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:9:p:3355-3372
    DOI: 10.1016/j.spa.2015.04.009
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    References listed on IDEAS

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    1. Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
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    Cited by:

    1. Xiong, Jie & Yang, Xu, 2019. "Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2681-2722.
    2. Yue Li & Shijie Shang & Jianliang Zhai, 2024. "Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$\mathbb {R}$$ R Driven by Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3496-3539, November.

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