Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

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

Keywords: branching processes , decreasing random migration , limit distributions

Rights: Copyright © 1985 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.13 • No. 3 • August, 1985
Back to Top