On Extremes of Random Clusters and Marked Renewal Cluster Processes (CROSBI ID 328014)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Basrak, Bojan ; Milinčević, Nikolina ; Žugec, Petra
engleski
On Extremes of Random Clusters and Marked Renewal Cluster Processes
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.
Renewal cluster processes ; Poisson cluster processes ; Hawkes process ; maximal claim size ; extreme value distributions ; random maxima ; limit theorems
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Podaci o izdanju
60 (2)
2023.
367-381
objavljeno
0021-9002
1475-6072
10.1017/jpr.2022.52