We derive a large deviation principle for the occupation time
func-tional, acting on functions with zero Lebesgue integral, for both
super-Brownian motion and critical branching Brownian motion in three
dimensions. Our technique, based on a moment formula of Dynkin, allows us to
compute the exact rate functions, which differ for the two processes. Obtaining
the exact rate function for the super-Brownian motion solves a conjecture of
Lee and Remillard. We also show the corresponding CLT and obtain similar
results for the superprocesses and critical branching process built over the
symmetric stable process of index $\beta$ in $R^d$, with $d < 2\beta < 2
+ d$ .
Publié le : 1998-04-14
Classification:
Occupation time,
large deviations,
branching Brownian motion,
super-Brownian motion,
60F10,
60J80,
60G57,
60J65,
60J55
@article{1022855645,
author = {Deuschel, Jean-Dominique and Rosen, Jay},
title = {Occupation time large deviations for critical branching Brownian
motion, super-Brownian motion and related processes},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 602-643},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855645}
}
Deuschel, Jean-Dominique; Rosen, Jay. Occupation time large deviations for critical branching Brownian
motion, super-Brownian motion and related processes. Ann. Probab., Tome 26 (1998) no. 1, pp. 602-643. http://gdmltest.u-ga.fr/item/1022855645/