## The Annals of Probability

### Occupation Times for Critical Branching Brownian Motions

#### 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

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