OCCUPATION TIME FLUCTUATIONS OF POISSON AND EQUILIBRIUM
FINITE VARIANCE BRANCHING SYSTEMS
Abstract: Functional limit theorems are presented for the rescaled occupation time
fluctuation process of a critical finite variance branching particle system in
with symmetric
-stable motion
starting off from either a standard Poisson random field or from the equilibrium distribution for intermediate
dimensions .
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.