A Cluster Limit Theorem for Infinitely Divisible Point Processes

Raluca Balan; Sana Louhichi

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arXiv · 0911.5471

A Cluster Limit Theorem for Infinitely Divisible Point Processes

Raluca Balan·Sana Louhichi

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Abstract

In this article, we consider a sequence $(N_n)_{n \geq 1}$ of point processes, whose points lie in a subset $E$ of $\bR \verb2\2 \{0\}$, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient conditions for the convergence in distribution of $(N_n)_{n \geq 1}$ to an infinitely divisible point process $N$. As applications, we discuss the exceedance processes and point processes based on regularly varying sequences.

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BibTeX RIS

Raluca Balan, Sana Louhichi. 2010-11-16. A Cluster Limit Theorem for Infinitely Divisible Point Processes. https://arxiv.org/abs/0911.5471

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