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Asymptotic Properties of the Markov Branching Process with Immigration

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Abstract

We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition function and on its asymptotic behavior. Conditional limit theorems for the population size are given in cases for which the transition function is dishonest.

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Authors and Affiliations

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

    Junping Li

  2. Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK

    Anyue Chen

  3. Department of Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, China

    Anyue Chen

  4. School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Anthony G. Pakes

Authors
  1. Junping Li
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  2. Anyue Chen
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  3. Anthony G. Pakes
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Correspondence to Anyue Chen.

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Li, J., Chen, A. & Pakes, A.G. Asymptotic Properties of the Markov Branching Process with Immigration. J Theor Probab 25, 122–143 (2012). https://doi.org/10.1007/s10959-010-0301-z

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  • DOI: https://doi.org/10.1007/s10959-010-0301-z

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