Linear-fractional branching processes with countably many types

Serik Sagitov

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arXiv · 1111.4689

Linear-fractional branching processes with countably many types

Serik Sagitov

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Abstract

We study multi-type Bienaym\'e-Galton-Watson processes with linear-fractional reproduction laws using various analytical tools like contour process, spinal representation, Perron-Frobenius theorem for countable matrices, 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.

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Serik Sagitov. 2011-11-20. Linear-fractional branching processes with countably many types. https://arxiv.org/abs/1111.4689

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