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September 2006 On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
Leonid Mytnik, Edwin Perkins, Anja Sturm
Ann. Probab. 34(5): 1910-1959 (September 2006). DOI: 10.1214/009117906000000331


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 Hölder continuity of the solutions near zero is established.


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Leonid Mytnik. Edwin Perkins. Anja Sturm. "On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients." Ann. Probab. 34 (5) 1910 - 1959, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1108.60057
MathSciNet: MR2271487
Digital Object Identifier: 10.1214/009117906000000331

Primary: 60H15 , 60K35
Secondary: 60F05 , 60J80 , 60K37

Keywords: colored noise , existence , heat equation , Stochastic partial differential equation , uniqueness

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 5 • September 2006
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