The Annals of Probability

Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes

Jean-Dominique Deuschel and Jay Rosen

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

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Ann. Probab., Volume 26, Number 2 (1998), 602-643.

First available in Project Euclid: 31 May 2002

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G57: Random measures
Secondary: 60J65: Brownian motion [See also 58J65] 60J55: Local time and additive functionals

Occupation time large deviations branching Brownian motion super-Brownian motion


Deuschel, Jean-Dominique; Rosen, Jay. Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes. Ann. Probab. 26 (1998), no. 2, 602--643. doi:10.1214/aop/1022855645.

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