Occupation time fluctuations of Poisson and equilibrium finite variance branching systems

Piotr Milos

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Occupation time fluctuations of Poisson and equilibrium finite variance branching systems

Piotr Milos

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Abstract

Functional limit theorems are presented for the rescaled occupation time fluctuations process of a critical finite variance branching particle system in $R^d$ with symmetric a-stable motion starting off from either a standard Poisson random field or from the equilibrium distribution for intermediate dimensions a<d<2a. The limit processes are determined sub-fractional and fractional Brownian motion respectively.

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Piotr Milos. 2006-05-12. Occupation time fluctuations of Poisson and equilibrium finite variance branching systems. https://arxiv.org/abs/math/0512414

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