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Critical Branching Processes with Random Migration

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Branching Processes

Part of the book series: Lecture Notes in Statistics ((LNS,volume 99))

Abstract

A new class of branching processes allowing a random migration component in every generation is considered: with probability p two types of emigration are possible — a random number of families and a random number of individuals, or with probability q there is not any migration (i.e. the process develops like a Bienaymé-Galton-Watson process), or with probability r a state-dependent immigration of new individuals is available, p + q + r = 1. The coresponding processes stopped at zero are studied in the critical case and the asymptotic behaviour of the non-extinction probability is obtained (depending on the range of an extra critical parameter).

Supported by the National Foundation for Scientific Investigations, grant MM-4/91.

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Author information

Authors and Affiliations

  1. Department of Probability and Statistics, Institute of Mathematics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    George P. Yanev & Nickolay M. Yanev

Authors
  1. George P. Yanev
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  2. Nickolay M. Yanev
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Editor information

Editors and Affiliations

  1. Stochastic Analysis Group, CMA, Australian National University, Canberra, ACT, 0200, Australia

    C. C. Heyde

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© 1995 Springer-Verlag New York, Inc.

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Yanev, G.P., Yanev, N.M. (1995). Critical Branching Processes with Random Migration. In: Heyde, C.C. (eds) Branching Processes. Lecture Notes in Statistics, vol 99. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2558-4_5

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  • DOI: https://doi.org/10.1007/978-1-4612-2558-4_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97989-2

  • Online ISBN: 978-1-4612-2558-4

  • eBook Packages: Springer Book Archive

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