Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: The white noise case

Leonid Mytnik; Edwin Perkins

doi:10.1007/s00440-009-0241-7

Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: The white noise case

Leonid Mytnik, Edwin Perkins

Data and Decision Sciences

Technion - Israel Institute of Technology

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

Abstract

We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Hölder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.

Original language	English
Pages (from-to)	1-96
Number of pages	96
Journal	Probability Theory and Related Fields
Volume	149
Issue number	1
DOIs	https://doi.org/10.1007/s00440-009-0241-7
State	Published - Mar 2011

Keywords

Pathwise uniqueness
Stochastic partial differential equations
White noise

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-009-0241-7

Cite this

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title = "Pathwise uniqueness for stochastic heat equations with H{\"o}lder continuous coefficients: The white noise case",

abstract = "We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is H{\"o}lder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.",

keywords = "Pathwise uniqueness, Stochastic partial differential equations, White noise",

author = "Leonid Mytnik and Edwin Perkins",

note = "Funding Information: L. Mytnik was supported in part by the Israel Science Foundation (grant No. 1162/06). Funding Information: E. Perkins was supported by an NSERC Research grant.",

year = "2011",

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doi = "10.1007/s00440-009-0241-7",

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AU - Perkins, Edwin

N1 - Funding Information: L. Mytnik was supported in part by the Israel Science Foundation (grant No. 1162/06). Funding Information: E. Perkins was supported by an NSERC Research grant.

PY - 2011/3

Y1 - 2011/3

N2 - We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Hölder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.

AB - We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Hölder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada-Watanabe argument for ordinary stochastic differential equations.

KW - Pathwise uniqueness

KW - Stochastic partial differential equations

KW - White noise

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U2 - 10.1007/s00440-009-0241-7

DO - 10.1007/s00440-009-0241-7

M3 - مقالة

SN - 0178-8051

VL - 149

SP - 1

EP - 96

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

ER -

Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: The white noise case

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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