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October 2000 Uniqueness for a class of one-dimensional stochastic PDEs using moment duality
Siva Athreya, Roger Tribe
Ann. Probab. 28(4): 1711-1734 (October 2000). DOI: 10.1214/aop/1019160504

Abstract

We establish a duality relation for the moments of bounded solutions to a class of one-dimensional parabolic stochastic partial differential equations. The equations are driven by multiplicative space-time white noise, with a non-Lipschitz multiplicative functional. The dual process is a system of branching Brownian particles. The same method can be applied to show uniqueness in law for a class of non-Lipschitz finite dimensional stochastic differential equations.

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Siva Athreya. Roger Tribe. "Uniqueness for a class of one-dimensional stochastic PDEs using moment duality." Ann. Probab. 28 (4) 1711 - 1734, October 2000. https://doi.org/10.1214/aop/1019160504

Information

Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60048
MathSciNet: MR1813840
Digital Object Identifier: 10.1214/aop/1019160504

Subjects:
Primary: 60H15

Keywords: Duality , Stochastic partial differential equations , uniqueness

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 4 • October 2000
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