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Uniqueness and Extinction of Weighted Markov Branching Processes

Anyue Chen (), Junping Li () and N. I. Ramesh ()
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Anyue Chen: The University of Greenwich
Junping Li: The University of Greenwich
N. I. Ramesh: The University of Greenwich

Methodology and Computing in Applied Probability, 2005, vol. 7, issue 4, 489-516

Abstract: Abstract This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained.

Keywords: Markov branching process; weighted Markov branching process; regularity and uniqueness; extinction; explosion (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s11009-005-5005-y

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