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April 1998 Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes
Jean-Dominique Deuschel, Jay Rosen
Ann. Probab. 26(2): 602-643 (April 1998). DOI: 10.1214/aop/1022855645

Abstract

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 $d < 2\beta < 2 + d$ .

Citation

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Jean-Dominique Deuschel. Jay Rosen. "Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes." Ann. Probab. 26 (2) 602 - 643, April 1998. https://doi.org/10.1214/aop/1022855645

Information

Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0962.60013
MathSciNet: MR1626503
Digital Object Identifier: 10.1214/aop/1022855645

Subjects:
Primary: 60F10, 60G57, 60J80
Secondary: 60J55, 60J65

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 1998
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