# Probabilistic approach in weighted Markov branching processes

Chen, Anyue, Li, Junping and Ramesh, N.I.
(2007)
*Probabilistic approach in weighted Markov branching processes.*
Statistics & Probability Letters, 78 (6).
pp. 771-779.
ISSN 0167-7152
(doi:10.1016/j.spl.2007.09.043)

## 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.

Item Type: | Article |
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Additional Information: | [1] Available online 26 October 2007. |

Uncontrolled Keywords: | compound Poisson process, hitting times, Markov branching process, random time change, uniqueness, weighted Markov branching process, |

Subjects: | Q Science > QA Mathematics |

Pre-2014 Departments: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Mathematical Sciences School of Computing & Mathematical Sciences > Statistics & Operational Research Group |

Related URLs: | |

Last Modified: | 14 Oct 2016 09:03 |

URI: | http://gala.gre.ac.uk/id/eprint/1258 |

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