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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 28, Fasc. 2,
pages 235 - 256
 

OCCUPATION TIME FLUCTUATIONS OF POISSON AND EQUILIBRIUM BRANCHING SYSTEMS IN CRITICAL AND LARGE DIMENSIONS

Piotr Miłoś

Abstract: Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in Rd  with symmetric a -stable motion starting off from either a standard Poisson random field or the equilibrium distribution for critical d = 2a and large d > 2a dimensions. The limit processes are generalised Wiener processes. The obtained convergence is in space-time and finite-dimensional distributions sense. Under the additional assumption on the branching law we obtain functional convergence.

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

Keywords and phrases: Functional central limit theorem; occupation time fluctuations; branching particles systems; generalised Wiener process; equilibrium distribution.

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