IJPAM: Volume 101, No. 7 (2015)

A MATURITY-DEPENDENT MARKOV BRANCHING
PROCESS WITH IMMIGRATION

T. Karthikeyan$^1$, J. Viswanath$^2$
$^{1,2}$Department of Mathematics
Veltech Technical University
Avadi, Chennai, 600 062, INDIA


Abstract. Parthasarathy [#!Parthasarathy!#] considered a Markov branching process in which each particle surviving at least up to a definite time $T$ splits into several particles at a later time $t$ $(t>T)$ while all particles whose life-time ends before the time $T$ leave no descendents. He calls $T$ as the maturity age of the particles. This type of maturity dependent branching has not been studied yet in Markov branching processes with immigration. To fill this gap, we investigate in the present paper a model of Markov branching processes which incorporates immigration and maturity-dependent branching.

Received: March 12, 2015

AMS Subject Classification: 60J80

Key Words and Phrases: Markov branching process, maturity-dependent splitting, immigration

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DOI: 10.12732/ijpam.v101i7.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 7
Pages: 673 - 683


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