Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction

Chen, AY, Pollett, P, Li, JP and Zhang, HJ (2010) Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction. Methodology And Computing In Applied Probability, 12 3: 511-531. doi:10.1007/s11009-009-9121-y


Author Chen, AY
Pollett, P
Li, JP
Zhang, HJ
Title Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction
Journal name Methodology And Computing In Applied Probability   Check publisher's open access policy
ISSN 1387-5841
1573-7713
Publication date 2010-09
Year available 2009
Sub-type Article (original research)
DOI 10.1007/s11009-009-9121-y
Volume 12
Issue 3
Start page 511
End page 531
Total pages 21
Place of publication New York, United States
Publisher Springer New York
Collection year 2011
Language eng
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. © 2009 Springer Science+Business Media, LLC.
Keyword Markov branching process
Pairwise interaction
Regularity
Uniqueness
Extinction
Explosion
Hitting times
Renewal sequence
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Available online: 11 February 2009

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
 
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Created: Sun, 25 Jul 2010, 00:04:12 EST