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Supercritical Branching Processes: A Unified Approach

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Book cover Branching Processes

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

Abstract

This paper gives a unified probabilistic approach to the limit theory of finite offspring mean supercritical branching processes. It is shown that the key to the convergence in probability of suitably normed branching processes is a law of large numbers for a triangular array of independent random variables. Criteria for convergence together with characterisations of the norming constants and limiting distributions follow from this property. The models considered include the Galton-Watson and the general age-dependent both in the simple and multitype case as well as in the varying and random environment settings. A martingale derived from a weakly convergent subsequence is essential in the proofs.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Melbourne, Parkville, Victoria, 3052, Australia

    Harry Cohn

Authors
  1. Harry Cohn
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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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Cohn, H. (1995). Supercritical Branching Processes: A Unified Approach. 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_1

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  • DOI: https://doi.org/10.1007/978-1-4612-2558-4_1

  • 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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