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A Conceptual Proof of the Kesten-Stigum Theorem for Multi-Type Branching Processes

  • Thomas Kurtz
  • Russell Lyons
  • Robin Pemantle
  • Yuval Peres
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)

Abstract

We give complete proofs of the theorem of convergence of types and the Kesten-Stigum theorem for multi-type branching processes. Very little analysis is used beyond the strong law of large numbers and some basic measure theory.

AMS(MOS) subject classifications. Primary 60J80.

Key words and phrases

Galton-Watson size-biased distribution 

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References

  1. [1]
    Athreya, K. B. and Ney, P. (1972) Branching Processes. Springer, New York.zbMATHCrossRefGoogle Scholar
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    Durrett, R. (1991) Probability: Theory and Examples. Wadsworth, Pacific Grove, California.Google Scholar
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    Kesten, H. and Stigum, B. (1966) A limit theorem for multidimensional Galton-Watson processes. Ann. Math. Statist. 37 1211–1223.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Kurtz, T. G. (1973) Almost sure convergence of the type distribution for a supercritical branching process, unpublished manuscript. Google Scholar
  5. [5]
    Lyons, R., Pemantle, R. Peres, Y. (1995) Conceptual proofs of LlogL criteria for mean behavior of branching processes, Ann. Probab. 23 1125–1138.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Thomas Kurtz
    • 1
  • Russell Lyons
    • 2
  • Robin Pemantle
    • 1
  • Yuval Peres
    • 3
  1. 1.Department of MathematicsUniversity of WisconsinMadison
  2. 2.Department of MathematicsIndiana UniversityBloomington
  3. 3.Department of StatisticsUniversity of CaliforniaBerkeley

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