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Contents of PMS, Vol. 27, Fasc. 2,
pages 181 - 203
 

OCCUPATION TIME FLUCTUATIONS OF POISSON AND EQUILIBRIUM FINITE VARIANCE BRANCHING SYSTEMS

Piotr Miloś

Abstract: Functional 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 from the equilibrium distribution for intermediate dimensions $\alpha < d < 2\alpha $. The limit processes are determined by sub-fractional and fractional Brownian motions, respectively.

2000 AMS Mathematics Subject Classification: Primary: 60F17, 60G20; Secondary: 60G15.

Key words and phrases: Functional central limit theorem; branching particles systems; occupation time fluctuations; fractional Brownian motion; sub-fractional Brownian motion; equilibrium distribution.

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