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Linear-fractional branching processes with countably many types

Serik Sagitov (Institutionen för matematiska vetenskaper, matematisk statistik)
Stochastic Processes and Their Applications (0304-4149). Vol. 123 (2013), 8, p. 2940-2956.
[Artikel, refereegranskad vetenskaplig]

We study multi-type Bienayme-Galton-Watson processes with linear-fractional reproduction laws using various analytical tools like the contour process, spinal representation, Perron-Frobenius theorem for countable matrices, and renewal theory. For this special class of branching processes with countably many types we present a transparent criterion for R-positive recurrence with respect to the type space. This criterion appeals to the Malthusian parameter and the mean age at childbearing of the associated linear-fractional Crump-Mode-Jagers process.

Nyckelord: Multivariate linear-fractional distribution; Contour process; Spinal representation; Bienayme-Galton-Watson process; Crump-Mode-Jagers process; Malthusian parameter; Perron-Frobenius theorem; R-positive recurrence; Renewal theory

Denna post skapades 2013-08-02. Senast ändrad 2017-09-14.
CPL Pubid: 180440


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Institutioner (Chalmers)

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


Matematisk statistik

Chalmers infrastruktur



Denna publikation är ett resultat av följande projekt:

Stochastic models of gene and species trees (VR//2010-5623)