Occupation time fluctuation limits of infinite variance equilibrium branching systems

2008/02/01 by Milos, Piotr
#60F17 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0802.0187

Abstract

We establish limit theorems for the fluctuations of the rescaled occupation time of a (d,α,β)-branching particle system. It consists of particles moving according to a symmetric α-stable motion in ℝ^d. The branching law is in the domain of attraction of a (1+β)-stable law and the initial condition is an equilibrium random measure for the system (defined below). In the paper we treat separately the cases of intermediate α/β(1+β)α/β dimensions. In the most interesting case of intermediate dimensions we obtain a version of a fractional stable motion. The long-range dependence structure of this process is also studied. Contrary to this case, limit processes in critical and large dimensions have independent increments.

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