Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-09T01:32:22.975Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on the Uniqueness of Weighted Markov Branching Processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Anyue Chen ,
Phil Pollett ,
Junping Li  and
Hanjun Zhang
Anyue Chen*
Affiliation:
The University of Hong Kong and The University of Greenwich
Phil Pollett*
Affiliation:
The University of Queensland
Junping Li*
Affiliation:
Central South University, Changsha
Hanjun Zhang*
Affiliation:
The University of Queensland
*
∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia.
∗∗∗∗ Postal address: School of Mathematical Sciences and Computing Technology, Central South University, Changsha, 410075, P. R. China. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present an elegant uniqueness criterion for the weighted Markov branching process in the potentially explosive case.

Keywords

Markov branching processregularityuniqueness

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 279 - 283
Copyright
Copyright © Applied Probability Trust 2007 

References

Anderson, W. J. (1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer, New York.CrossRefGoogle Scholar
Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhäuser, Boston, MA.Google Scholar
Athreya, K. B. and Jagers, P. (1997). Classical and Modern Branching Processes. Springer, Berlin.Google Scholar
Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, Berlin.Google Scholar
Chen, A., Pollett, P., Zhang, H. and Cairns, B. (2005). Uniqueness criteria for continuous-time Markov chains with general transition structure. Adv. Appl. Prob. 37, 1056–1074.Google Scholar
Chen, A. Y. (2002a). Ergodicity and stability of generalized Markov branching processes with resurrection. J. Appl. Prob. 39, 786–803.Google Scholar
Chen, A. Y. (2002b). Uniqueness and extinction properties of generalized Markov branching processes. J. Math. Anal. Appl. 274, 482–494.CrossRefGoogle Scholar
Chen, M. F. (1992). From Markov Chains to Non-Equilibrium Particle Systems. World Scientific, Singapore.CrossRefGoogle Scholar
Chen, R. R. (1997). An extended class of time-continuous branching processes. J. Appl. Prob. 34, 14–23.Google Scholar
Harris, T. H. (1963). The Theory of Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
Yang, X. Q. (1990). The Construction Theory of Denumerable Markov Processes. John Wiley, Chichester.Google Scholar