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Uniqueness and Extinction of Weighted Markov Branching Processes

Author

Listed:
  • Anyue Chen

    (The University of Greenwich
    University of Hong Kong)

  • Junping Li

    (The University of Greenwich
    Central South University)

  • N. I. Ramesh

    (The University of Greenwich)

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.

Suggested Citation

  • Anyue Chen & Junping Li & N. I. Ramesh, 2005. "Uniqueness and Extinction of Weighted Markov Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 489-516, December.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:4:d:10.1007_s11009-005-5005-y
    DOI: 10.1007/s11009-005-5005-y
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    Cited by:

    1. Chen, Anyue & Li, Junping & Ramesh, N.I., 2008. "Probabilistic approach in weighted Markov branching processes," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 771-779, April.
    2. Li Junping & Chen Anyue, 2013. "The Decay Parameter and Invariant Measures for Markovian Bulk-Arrival Queues with Control at Idle Time," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 467-484, June.
    3. Anyue Chen & Phil Pollett & Junping Li & Hanjun Zhang, 2010. "Uniqueness, Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 511-531, September.

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