Uniqueness, Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction

Anyue Chen (), Phil Pollett (), Junping Li () and Hanjun Zhang ()
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Anyue Chen: The University of Liverpool
Phil Pollett: University of Queensland
Junping Li: Central South University
Hanjun Zhang: Xiangtan University

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 3, 511-531

Abstract: Abstract We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities, the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression for mean explosion time is established.

Keywords: Markov branching process; Pairwise interaction; Regularity; Uniqueness; Extinction; Explosion; Hitting times; Renewal sequence; Primary 60J27; Secondary 60J80 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-009-9121-y

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