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August, 1985 Critical Branching Processes with Nonhomogeneous Migration
N. M. Yanev, K. V. Mitov
Ann. Probab. 13(3): 923-933 (August, 1985). DOI: 10.1214/aop/1176992914


This paper deals with a modification of Galton-Watson processes allowing random migration in the following way: with a probability $p_n$(in the nth generation) one particle is eliminated and does not take part in further evolution, or with a probability $r_n$ takes place immigration of new particles according to a p.g.f. $G(s)$, and, finally, with a probability $q_n$ there is not any migration, $p_n + q_n + r_n = 1, n = 0, 1, 2, \cdots$. We investigate a critical case when the offspring mean is equal to one and $r_nG'(1) \equiv p_n \rightarrow 0$. Depending on the rate of this convergence we obtain different types of limit theorems.


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N. M. Yanev. K. V. Mitov. "Critical Branching Processes with Nonhomogeneous Migration." Ann. Probab. 13 (3) 923 - 933, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0576.60077
MathSciNet: MR799428
Digital Object Identifier: 10.1214/aop/1176992914

Primary: 60J80
Secondary: 60J85 , 92A10 , 92A15

Keywords: branching processes , decreasing random migration , limit distributions

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
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