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Alternating branching processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Penka Mayster
Penka Mayster*
Affiliation:
University of Tunis
*
∗Postal address: Institut Supérieur des Etudes Technologiques de Radès, Rue Jérusalem-Radès, B.P. 172, Radès Médina 2098, Tunisia. Email address: [email protected]
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Abstract

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We introduce the idea of controlling branching processes by means of another branching process, using the fractional thinning operator of Steutel and van Harn. This idea is then adapted to the model of alternating branching, where two Markov branching processes act alternately at random observation and treatment times. We study the extinction probability and limit theorems for reproduction by n cycles, as n → ∞.

Keywords

Controlled branching processstate-dependent emigrationrandom environmentextinction probabilitylimit theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K05: Renewal theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1095 - 1108
Copyright
© Applied Probability Trust 2005 

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