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Heavy-Tailed Branching Process with Immigration (CROSBI ID 213373)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Basrak, Bojan ; Kulik, Rafał ; Palmowski, Zbigniew Heavy-Tailed Branching Process with Immigration // Stochastic models, 29 (2013), 4; 413-434. doi: 10.1080/15326349.2013.838508

Podaci o odgovornosti

Basrak, Bojan ; Kulik, Rafał ; Palmowski, Zbigniew

engleski

Heavy-Tailed Branching Process with Immigration

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.

Branching process with immigration ; INAR ; Regularly varying distribution

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Podaci o izdanju

29 (4)

2013.

413-434

objavljeno

1532-6349

1532-4214

10.1080/15326349.2013.838508

Povezanost rada

Matematika

Poveznice
Indeksiranost