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Probabilistic approach in weighted Markov branching processes

Author

Listed:
  • Chen, Anyue
  • Li, Junping
  • Ramesh, N.I.

Abstract

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily 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 the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:771-779
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    References listed on IDEAS

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    1. 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.
    2. Chen, Anyue & Li, Junping & Ramesh, N.I., 2006. "General Harris regularity criterion for non-linear Markov branching processes," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 446-452, March.
    3. Helland, Inge S., 1978. "Continuity of a class of random time transformations," Stochastic Processes and their Applications, Elsevier, vol. 7(1), pages 79-99, March.
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    Cited by:

    1. Li, Pei-Sen, 2019. "A continuous-state polynomial branching process," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2941-2967.

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