## The Annals of Probability

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

Jie Xiong

#### 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

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
Secondary: 60J68: Superprocesses

#### 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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