A Cluster Limit Theorem for Infinitely Divisible Point Processes

2009/11/29 by Balan, Raluca, Louhichi, Sana
#60G55 #60G70 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0911.5471

Abstract

In this article, we consider a sequence (N_n)_{n ≥ 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 ≥ 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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