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

Leonid Mytnik; Eyal Neuman

doi:https://doi.org/10.1016/j.spa.2015.04.009

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

Leonid Mytnik, Eyal Neuman

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3355-3372
Number of pages	18
Journal	Stochastic Processes and their Applications
Volume	125
Issue number	9
DOIs	https://doi.org/10.1016/j.spa.2015.04.009
State	Published - 1 Sep 2015

Keywords

Pathwise uniqueness
Stochastic partial differential equations
White noise

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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https://doi.org/10.1016/j.spa.2015.04.009

Cite this

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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 H{\"o}lder 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 H{\"o}lder continuous.",

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AU - Neuman, Eyal

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N2 - 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.

AB - 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.

KW - Pathwise uniqueness

KW - Stochastic partial differential equations

KW - White noise

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DO - https://doi.org/10.1016/j.spa.2015.04.009

M3 - مقالة

SN - 0304-4149

VL - 125

SP - 3355

EP - 3372

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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