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Convergence of critical multitype Galton-Watson branching processes

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  • Nakagawa, Tetsuo

Abstract

Allowing an offspring probability distribution that has infinite variances, we establish the convergence in finite-dimensional distributions of normalized critical multitype Galton-Watson branching processes with increasing initial population size in the two cases of not conditioning and of conditioning on non-extinction of the processes in the nth generation. Furthermore, if the offspring probability distribution has only finite variances, we show that some linear functions of the above processes weakly converge to the diffusions given by Feller, and by Lamperti and Ney.

Suggested Citation

  • Nakagawa, Tetsuo, 1986. "Convergence of critical multitype Galton-Watson branching processes," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 269-279, December.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:2:p:269-279
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    Cited by:

    1. Yang, Hui, 2019. "Scaling limit of the local time of the reflected (1,2)-random walk," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.

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