Super-Brownian motion as the unique strong solution to an SPDE
Jie Xiong
TL;DR
This paper derives an SPDE for super-Brownian motion and proves strong uniqueness of its solutions using an extended Yamada-Watanabe argument, also applying similar results to the Fleming-Viot process.
Contribution
It introduces a new SPDE formulation for super-Brownian motion and establishes strong uniqueness, extending the Yamada-Watanabe approach to measure-valued processes.
Findings
Established strong uniqueness for the SPDE of super-Brownian motion
Extended Yamada-Watanabe argument applicable to measure-valued processes
Similar results proved for the Fleming-Viot process
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.
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