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General collision branching processes with two parameters

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Abstract

A new class of branching models, the general collision branching processes with two parameters, is considered in this paper. For such models, it is necessary to evaluate the absorbing probabilities and mean extinction times for both absorbing states. Regularity and uniqueness criteria are firstly established. Explicit expressions are then obtained for the extinction probability vector, the mean extinction times and the conditional mean extinction times. The explosion behavior of these models is investigated and an explicit expression for mean explosion time is established. The mean global holding time is also obtained. It is revealed that these properties are substantially different between the super-explosive and sub-explosive cases.

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Authors and Affiliations

  1. Department of Mathematical Sciences, the University of Liverpool, Liverpool, L69 7ZL, UK

    AnYue Chen

  2. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong

    AnYue Chen

  3. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, China

    JunPing Li

Authors
  1. AnYue Chen
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  2. JunPing Li
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Correspondence to JunPing Li.

Additional information

This work was partially supported by National Natural Science Foundation of China (Grant No. 10771216), Research Grants Council of Hong Kong (Grant No. HKU 7010/06P) and Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry of China (Grant No. [2007]1108)

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Chen, A., Li, J. General collision branching processes with two parameters. Sci. China Ser. A-Math. 52, 1546–1568 (2009). https://doi.org/10.1007/s11425-009-0129-0

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  • DOI: https://doi.org/10.1007/s11425-009-0129-0

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