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Multitype branching processes based on exact progeny lengths of particles in a Galton-Watson branching process

Published online by Cambridge University Press:  14 July 2016

V. G. Gadag  and
M. B. Rajarshi
V. G. Gadag*
Affiliation:
University of Poona
M. B. Rajarshi*
Affiliation:
University of Poona
*
∗On study leave from University of Poona. Presently at Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, N.S. Canada, B3H 3J5.
∗∗Postal address: Department of Statistics, University of Poona, Pune 411007, India.
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Abstract

In Gadag and Rajarshi (1987), we studied a bivariate (multitype) branching process based on infinite and finite lines of descent, of particles of a supercritical one-dimensional (multitype) Galton-Watson branching process (GWBP). In this paper, we discuss a few more meaningful and interesting univariate and multitype branching processes, based on exact progeny lengths of particles in a GWBP. Our constructions relax the assumption of supercriticality made in Gadag and Rajarshi (1987). We investigate some finite-time and asymptotic results of these processes in some details and relate them to the original process. These results are then used to propose new and better estimates of the offspring mean. An illustration based on the branching process of the white male population of the USA is also given. We believe that our work offers a rather finer understanding of the branching property.

Keywords

MULTITYPE GALTON-WATSON BRANCHING PROCESSFINITE AND INFINITE LINES OF DESCENTSTRONG CONVERGENCECENTRAL LIMIT THEOREMSESTIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 1 - 8
Copyright
Copyright © Applied Probability Trust 1989 

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