The Annals of Probability

Occupation Times for Critical Branching Brownian Motions

J. Theodore Cox and David Griffeath

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Abstract

We prove central limit theorems, strong laws, large deviation results, and a weak convergence theorem for suitably normalized occupation times of critical binary branching Brownian motions started from Poisson random fields on $R^d, d \geq 2$. The results are strongly dimension dependent. The main result (Theorem 2) asserts that in two dimensions, as opposed to all other dimensions, the average occupation time of a bounded set with positive measure converges in distribution to a nondegenerate limit.

Article information

Source
Ann. Probab., Volume 13, Number 4 (1985), 1108-1132.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992799

Digital Object Identifier
doi:10.1214/aop/1176992799

Mathematical Reviews number (MathSciNet)
MR806212

Zentralblatt MATH identifier
0582.60091

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Infinite particle system branching Brownian motion occupation times strong laws central limit theorems large deviations cumulants

Citation

Cox, J. Theodore; Griffeath, David. Occupation Times for Critical Branching Brownian Motions. Ann. Probab. 13 (1985), no. 4, 1108--1132. doi:10.1214/aop/1176992799. https://projecteuclid.org/euclid.aop/1176992799


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