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Geometric aspects of Fleming-Viot and Dawson-Watanabe processes. (English) Zbl 0895.60082

Summary: 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.

MSC:

60J60 Diffusion processes
60G57 Random measures
58J65 Diffusion processes and stochastic analysis on manifolds
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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