Open Access
November, 1985 Occupation Times for Critical Branching Brownian Motions
J. Theodore Cox, David Griffeath
Ann. Probab. 13(4): 1108-1132 (November, 1985). DOI: 10.1214/aop/1176992799


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.


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J. Theodore Cox. David Griffeath. "Occupation Times for Critical Branching Brownian Motions." Ann. Probab. 13 (4) 1108 - 1132, November, 1985.


Published: November, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0582.60091
MathSciNet: MR806212
Digital Object Identifier: 10.1214/aop/1176992799

Primary: 60K35

Keywords: Branching Brownian motion , central limit theorems , Cumulants , Infinite particle system , large deviations , Occupation times , strong laws

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 4 • November, 1985
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