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.
@article{1024404509,
author = {Schied, Alexander},
title = {Geometric aspects of Fleming-Viot and Dawson-Watanabe
processes},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1160-1179},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404509}
}
Schied, Alexander. Geometric aspects of Fleming-Viot and Dawson-Watanabe
processes. Ann. Probab., Tome 25 (1997) no. 4, pp. 1160-1179. http://gdmltest.u-ga.fr/item/1024404509/