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

Piotr Milos

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arXiv · 1001.5142

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

Piotr Milos

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Abstract

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, \alpha 0. 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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Piotr Milos. 2010-01-28. Fluctuations of the occupation times for branching system starting from infinitely divisible point processes. https://arxiv.org/abs/1001.5142

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