Occupation time fluctuations of Poisson and equilibrium finite variance branching systems
Abstract
Functional limit theorems are presented for the rescaled occupation time fluctuations 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 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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