General linear-fractional branching processes with discrete time

Alexey Lindo; Serik Sagitov

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arXiv · 1510.06859

General linear-fractional branching processes with discrete time

Alexey Lindo·Serik Sagitov

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Abstract

We study a linear-fractional Bienaymé-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads to the linear-fractional distribution formula for an arbitrary observation time, which allows us to establish transparent limit theorems for the subcritical, critical and supercritical cases. Our results extend recent findings for the linear-fractional branching processes with countably many types.

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Alexey Lindo, Serik Sagitov. 2016-03-03. General linear-fractional branching processes with discrete time. https://arxiv.org/abs/1510.06859

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