A branching process with a state dependent immigration component

1 January 1971

journal article
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 3 (2) , 301-314
https://doi.org/10.2307/1426173

Abstract

Consider the well known Galton-Watson branching process (Harris (1963)) in which individuals reproduce independently of each other and have probabilitya_j(j= 0, 1, · · ·) of giving rise tojindividuals 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,b_j(j= 0, 1, · · ·) being the probability ofjimmigrants entering each generation. For a review of this work see Seneta (1969), and Pakes (1971 a, b and c) for further results.

Keywords

This publication has 17 references indexed in Scilit:

On the critical Galton-Watson process with immigration
Journal of the Australian Mathematical Society, 1971
On a Theorem of Quine and Seneta for the Galton-Watson Process With Immigration
Australian Journal of Statistics, 1971
Extension of a Result of Seneta for the Super-Critical Galton-Watson Process
The Annals of Mathematical Statistics, 1970
A note on the supercritical Galton-Watson process with immigration
Mathematical Biosciences, 1970
A stochastic process whose successive intervals between events form a first order Markov chain — I
Journal of Applied Probability, 1968
On asymptotic properties of sub-critical branching processes
Journal of the Australian Mathematical Society, 1968
A Refinement of Two Theorems in the Theory of Branching Processes
Theory of Probability and Its Applications, 1967
The Galton-Watson Process with Mean One and Finite Variance
Theory of Probability and Its Applications, 1966
Zur biomathematischen Begründung der Verteilung der Elemente taxonomischer Einheiten des natürlichen Systems in einer logarithmischen Reihe
Biometrische Zeitschrift, 1959
On occupation times for Markoff processes
Transactions of the American Mathematical Society, 1957