Fluctuations of the occupation times for branching system starting from infinitely divisible point processes

Details Fluctuations of the occupation times for branching system starting from infinitely divisible point processes Fluctuations of the occupation times for branching system starting from infinitely divisible point processes

2010-01-28

arxiv.org/abs/1001.5142v2

Mathematics

Probability

Proofs shortened, extended discussion

Scientific paper

In the paper the rescaled occupation time fluctuation process of a certain empirical system is investigated. The system consists of particles evolving independently according to \alpha-stable motion in R^d, \alpha0. We study how the limit behaviour of the fluctuations of the occupation time depends on the \emph{initial particle configuration}. We obtain a functional central limit theorem for a vast class of infinitely divisible distributions. Our findings extend and put in a unified setting results which previously seemed to be disconnected. The limit processes form a one dimensional family of long-range dependance centred Gaussian processes.

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