A branching process with a state dependent immigration component

Author:

Pakes A. G.

Abstract

Consider the well known Galton-Watson branching process (Harris (1963)) in which individuals reproduce independently of each other and have probability aj (j = 0, 1, · · ·) of giving rise to j individuals in the next generation. In recent years some attention has been given to the branching process in which there is an independent immigration component at each generation, bj (j = 0, 1, · · ·) being the probability of j immigrants entering each generation. For a review of this work see Seneta (1969), and Pakes (1971 a, b and c) for further results.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Cited by 69 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Extinction behavior and recurrence of n-type Markov branching–immigration processes;Boundary Value Problems;2024-01-02

2. A Galton–Watson process with a threshold at 1 and an immigration at 0;Statistics & Probability Letters;2023-10

3. On supercritical branching processes with emigration;Journal of Applied Probability;2022-07-08

4. On central limit theorems for branching processes with dependent immigration;Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics;2020

5. Branching processes in varying environment with generation-dependent immigration;Stochastic Models;2019-03-07

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