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Dependence and interaction in branching processes

Peter Jagers (Institutionen för matematiska vetenskaper, matematisk statistik) ; Fima C. Klebaner
Springer Proceedings in Mathematics and Statistics (2194-1009). Vol. 33 (2013), p. 325-333.
[Konferensbidrag, refereegranskat]

Independence of reproducing individuals can be viewed as the very defining property of branching processes. It is crucial for the most famous results of the theory, the determination of the extinction probability and the dichotomy between extinction and exponential increase. In general processes, stabilisation of the age-distribution under growth follows, and indeed of the over-all population composition, and so do the many fine results of the area, like conditional stabilisation of the size of non-extinct subcritical processes. The last two decades have witnessed repeated attempts at treating branching processes with various kinds of dependence between individuals, ranging from local dependence between close relatives only to population size dependence. Of particular interest are very recent findings on processes that change from being supercritical to subcriticality at some threshold size, the carrying capacity of the habitat. We overview the development with an emphasis on these recent results.

Nyckelord: Age-structure, Carrying capacity, Dependence, General branching processes



Denna post skapades 2014-01-09. Senast ändrad 2016-08-18.
CPL Pubid: 191926

 

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Institutioner (Chalmers)

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

Ämnesområden

Sannolikhetsteori och statistik

Chalmers infrastruktur