The Annals of Probability

Geometric aspects of Fleming-Viot and Dawson-Watanabe processes

Alexander Schied

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This paper is concerned with the intrinsic metrics of the two main classes of superprocesses. For the Fleming-Viot process, we identify it as the Bhattacharya distance, and for Dawson-Watanabe processes, we find the Kakutani-Hellinger metric. The corresponding geometries are studied in some detail. In particular, representation formulas for geodesics and arc length functionals are obtained. The relations between the two metrics yield a geometric interpretation of the identification of the Fleming-Viot process as a Dawson-Watanabe superprocess conditioned to have total mass 1. As an application, a functional limit theorem for super-Brownian motion conditioned on local extinction is proved.

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Ann. Probab., Volume 25, Number 3 (1997), 1160-1179.

First available in Project Euclid: 18 June 2002

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Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65] 60G57: Random measures 58G32 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Intrinsic metric Fleming-Viot process Dawson-Watanabe superprocess Kakutani-Hellinger distance Bhattacharya metric


Schied, Alexander. Geometric aspects of Fleming-Viot and Dawson-Watanabe processes. Ann. Probab. 25 (1997), no. 3, 1160--1179. doi:10.1214/aop/1024404509.

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