Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions

Details Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions

2007-07-02

arxiv.org/abs/0707.0316v1

Prob. and Math. Stat. Vol. 278, Fasc. 2 (2008) pp. 235-256

Mathematics

Probability

Scientific paper

Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson random field or the equilibrium distribution for critical $d=2\alpha$ and large $d>2\alpha$ dimensions. The limit processes are generalised Wiener processes. The obtained convergence is in space-time, finite-dimensional distributions sense. With the addtional assumption on the branching law we obtain functional convergence.

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