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July 1997 Geometric aspects of Fleming-Viot and Dawson-Watanabe processes
Alexander Schied
Ann. Probab. 25(3): 1160-1179 (July 1997). DOI: 10.1214/aop/1024404509


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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Alexander Schied. "Geometric aspects of Fleming-Viot and Dawson-Watanabe processes." Ann. Probab. 25 (3) 1160 - 1179, July 1997.


Published: July 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0895.60082
MathSciNet: MR1457615
Digital Object Identifier: 10.1214/aop/1024404509

Primary: 58G32 , 60G57 , 60J60 , 60J80

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

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • July 1997
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