The Annals of Probability

Uniqueness for a class of one-dimensional stochastic PDEs using moment duality

Siva Athreya and Roger Tribe

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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.

Article information

Source
Ann. Probab., Volume 28, Number 4 (2000), 1711-1734.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160504

Digital Object Identifier
doi:10.1214/aop/1019160504

Mathematical Reviews number (MathSciNet)
MR1813840

Zentralblatt MATH identifier
1044.60048

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Stochastic partial differential equations Duality Uniqueness

Citation

Athreya, Siva; Tribe, Roger. Uniqueness for a class of one-dimensional stochastic PDEs using moment duality. Ann. Probab. 28 (2000), no. 4, 1711--1734. doi:10.1214/aop/1019160504. https://projecteuclid.org/euclid.aop/1019160504


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References

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