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A note on the multitype Markov branching process

Published online by Cambridge University Press:  14 July 2016

V. G. Gadag
V. G. Gadag*
Affiliation:
University of Poona
*
∗Postal address: Department of Statistics, University of Poona, Pune 411 007, India.
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Abstract

We consider a supercritical, p-dimensional Markov branching process (MBP). Based on the finite and the infinite lines of descent of particles of this p-dimensional MBP, we construct an associated 2p-dimensional process. We show that such a process is a 2p-dimensional, supercritical MBP. This 2p-dimensional process retains the branching property when conditioned on the sets of extinction and non-extinction. Asymptotic results and central limit theorems for the associated process and the original process are established by using the results of Gadag and Rajarshi (1987).

Keywords

FINITE AND INFINITE LINE OF DESCENTSUPERCRITICALNON-POSITIVE REGULAR PROCESSCENTRAL LIMIT THEOREM
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 631 - 636
Copyright
Copyright © Applied Probability Trust 1989 

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References

Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
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Gadag, V. G. and Kunte, S. (1980) Some results on the non-extinction paths of a supercritical Galton-Watson process. J. Indian Statist. Assoc. 18, 73–80.Google Scholar
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