Naslov
On Extremes of Random Clusters and Marked Renewal Cluster Processes

Autori
Basrak, Bojan ; Milinčević, Nikolina ; Žugec, Petra

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Journal of applied probability (2023)

Status rada
Prihvaćen

Ključne riječi
Renewal cluster processes ; Poisson cluster processes ; Hawkes process ; maximal claim size ; extreme value distributions ; random maxima ; limit theorems

Sažetak
The article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster and then we apply the developed theory to determine the limiting distribution of $\max\{; ; ; ; ; ; ; ; ; ; X_j: j=1, \ldots, K(t)\}; ; ; ; ; ; ; ; ; ; $, where $K(t)$ is the number of i.i.d. observations $(X_j)$ arriving up to the time $t$ according to a general marked renewal cluster process. The results are illustrated in the context of some commonly used Poisson cluster models such as the marked Hawkes process.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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