A Cluster-Limit Theorem for Infinitely Divisible Point Processes

Raluca Balan (1) , Sana Louhichi (2)

1 Department of Mathematics and Statistics [Ottawa]
2 IPS - Inférence Processus Stochastiques

In this article, we consider a sequence (N n ) n≥1 of point processes, whose points lie in a subset E of R\{0} and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient conditions for the convergence in the 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.

Mots clés: point process; infinite divisibility; weak dependence; exceedance process; extremal index

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Raluca Balan, Sana Louhichi. A Cluster-Limit Theorem for Infinitely Divisible Point Processes. Statistics, 2011, 45 (1), pp.3-18. ⟨10.1080/02331888.2010.541252⟩. ⟨hal-00851603⟩