On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

Leonid Mytnik; Edwin Perkins; Anja Sturm

doi:10.1214/009117906000000331

On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

Leonid Mytnik, Edwin Perkins, Anja Sturm

Data and Decision Sciences

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

Abstract

We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on ℝ^d for d ≥ 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.

Original language	English
Pages (from-to)	1910-1959
Number of pages	50
Journal	Annals of Probability
Volume	34
Issue number	5
DOIs	https://doi.org/10.1214/009117906000000331
State	Published - Sep 2006

Keywords

Colored noise
Existence
Heat equation
Stochastic partial differential equation
Uniqueness

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/009117906000000331

Cite this

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abstract = "We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on ℝd for d ≥ 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.",

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AB - We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on ℝd for d ≥ 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.

KW - Colored noise

KW - Existence

KW - Heat equation

KW - Stochastic partial differential equation

KW - Uniqueness

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JO - Annals of Probability

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On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

Abstract

Keywords

ASJC Scopus subject areas

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