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