Naslov
Heavy-Tailed Branching Process with Immigration

Autori
Basrak, Bojan ; Kulik, Rafał ; Palmowski, Zbigniew

Izvornik
Stochastic models (1532-6349) 29 (2013), 4; 413-434

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Branching process with immigration ; INAR ; Regularly varying distribution

Sažetak
In this paper we analyze a branching process with immigration defined recursively by Xt=θt∘Xt−1+Bt for a sequence (Bt) of i.i.d. random variables and random mappings θt∘x:=θt(x)=∑xi=1A(t)i, with (A(t)i)i∈N0 being a sequence of N0-valued i.i.d. random variables independent of Bt. We assume that one of generic variables A and B has a regularly varying tail distribution. We identify the tail behaviour of the distribution of the stationary solution Xt. We also prove CLT for the partial sums that could be further generalized to FCLT. Finally, we also show that partial maxima have a Fr\'echet limiting distribution.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA