The Annals of Probability

Super-Brownian motion as the unique strong solution to an SPDE

Jie Xiong

Full-text: Open access

Abstract

A stochastic partial differential equation (SPDE) is derived for super-Brownian motion regarded as a distribution function valued process. The strong uniqueness for the solution to this SPDE is obtained by an extended Yamada–Watanabe argument. Similar results are also proved for the Fleming–Viot process.

Article information

Source
Ann. Probab., Volume 41, Number 2 (2013), 1030-1054.

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1362750949

Digital Object Identifier
doi:10.1214/12-AOP789

Mathematical Reviews number (MathSciNet)
MR3077534

Zentralblatt MATH identifier
1266.60119

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60J68: Superprocesses

Keywords
Super Brownian motion Fleming–Viot process stochastic partial differential equation backward doubly stochastic differential equation strong uniqueness

Citation

Xiong, Jie. Super-Brownian motion as the unique strong solution to an SPDE. Ann. Probab. 41 (2013), no. 2, 1030--1054. doi:10.1214/12-AOP789. https://projecteuclid.org/euclid.aop/1362750949


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