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General branching processes in discrete time as random trees.

Peter Jagers (Institutionen för matematiska vetenskaper, matematisk statistik) ; Serik Sagitov (Institutionen för matematiska vetenskaper, matematisk statistik)
Bernoulli (1350-7265). Vol. 14 (2008), 4, p. 949-962.
[Artikel, refereegranskad vetenskaplig]

The simple Galton-Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of the family tree. This viewpoint has led to new insights and a revival of classical theory. We show how a similar reinterpretation can shed new light on the more interesting forms of branching processes that allow repeated bearings and, thus, overlapping generations. In particular, we use the stable pedigree law to give a transparent description of a size-biased version of general branching processes in discrete time. This allows us to analyse the xlog x condition for exponential growth of supercritical general processes, and also the relation between simple Galton-Watson and more general branching processes.

Nyckelord: random trees, size-biased distributions, Galton-Watson, Crump-Mode-Jagers



Denna post skapades 2008-11-10. Senast ändrad 2017-09-14.
CPL Pubid: 77532

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik
Annan biologi

Chalmers infrastruktur