Linear-fractional branching processes with countably many types

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Sagitov, Serik^1,2 

[1] Chalmers, Gothenburg, Sweden

[2] Univ Gothenburg, Gothenburg, Sweden

关键词: 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;   

DOI  :  10.1016/j.spa.2013.03.008

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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