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Multi-type branching in varying environment

Author

Listed:
  • Biggins, J. D.
  • Cohn, H.
  • Nerman, O.

Abstract

This paper considers the asymptotic theory of the varying environment Galton-Watson process with a countable set of types. This paper examines the convergence in Lp and almost surely of the numbers of the various types when normalised by the corresponding expected number. The harmonic functions of the mean matrices play a central role in the analysis. Many previously studied models provide particular cases.

Suggested Citation

  • Biggins, J. D. & Cohn, H. & Nerman, O., 1999. "Multi-type branching in varying environment," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 357-400, October.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:2:p:357-400
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    References listed on IDEAS

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    1. Biggins, J. D. & D'Souza, J. C., 1993. "The supercritical Galton-Watson process in varying environments--Seneta-Heyde norming," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 237-249, November.
    2. Biggins, J. D., 1990. "The central limit theorem for the supercritical branching random walk, and related results," Stochastic Processes and their Applications, Elsevier, vol. 34(2), pages 255-274, April.
    3. D'Souza, J. C. & Biggins, J. D., 1992. "The supercritical Galton-Watson process in varying environments," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 39-47, August.
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    Cited by:

    1. Onur Gün & Wolfgang König & Ozren Sekulović, 2015. "Moment Asymptotics for Multitype Branching Random Walks in Random Environment," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1726-1742, December.
    2. Vincent Bansaye, 2019. "Ancestral Lineages and Limit Theorems for Branching Markov Chains in Varying Environment," Journal of Theoretical Probability, Springer, vol. 32(1), pages 249-281, March.
    3. Vincent Bansaye & Alain Camanes, 2018. "Queueing for an infinite bus line and aging branching process," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 99-138, February.

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