The Annals of Probability

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

Jie Xiong

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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

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

First available in Project Euclid: 8 March 2013

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Zentralblatt MATH identifier

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

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


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.

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