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A Remark on the Uniqueness of Weighted Markov Branching Processes

  • Anyue Chen (a1), Phil Pollett (a2), Junping Li (a3) and Hanjun Zhang (a2)

Abstract

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

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Copyright

Corresponding author

Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: achen@hkucc.hku.hk
∗∗ Postal address: Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia.
∗∗∗ Email address: pkp@maths.uq.edu.au
∗∗∗∗ Postal address: School of Mathematical Sciences and Computing Technology, Central South University, Changsha, 410075, P. R. China. Email address: jpli@mail.csu.edu.cn
∗∗∗∗ Email address: hjz@maths.uq.edu.au

References

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Anderson, W. J. (1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer, New York.
Asmussen, S. and Hering, H. (1983). Branching Processes. Birkhäuser, Boston, MA.
Athreya, K. B. and Jagers, P. (1997). Classical and Modern Branching Processes. Springer, Berlin.
Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, Berlin.
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, 10561074.
Chen, A. Y. (2002a). Ergodicity and stability of generalized Markov branching processes with resurrection. J. Appl. Prob. 39, 786803.
Chen, A. Y. (2002b). Uniqueness and extinction properties of generalized Markov branching processes. J. Math. Anal. Appl. 274, 482494.
Chen, M. F. (1992). From Markov Chains to Non-Equilibrium Particle Systems. World Scientific, Singapore.
Chen, R. R. (1997). An extended class of time-continuous branching processes. J. Appl. Prob. 34, 1423.
Harris, T. H. (1963). The Theory of Branching Processes. Springer, Berlin.
Yang, X. Q. (1990). The Construction Theory of Denumerable Markov Processes. John Wiley, Chichester.

Keywords

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A Remark on the Uniqueness of Weighted Markov Branching Processes

  • Anyue Chen (a1), Phil Pollett (a2), Junping Li (a3) and Hanjun Zhang (a2)

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