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Asymptotic properties of subcritical Galton-Watson processes

  • J. H. Bagley (a1)

Abstract

Results connecting Yaglom's limit and Z1 are obtained. For example, if α > 1, E[Z α 1] and converge or diverge together.

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Postal address: Statistical Laboratory, Department of Mathematics, University of Manchester, Manchester M13 9PL, U.K.

References

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[1] Bingham, N. H. and Doney, R. A. (1974) Asymptotic properties of supercritical branching processes. I: The Galton–Watson process. Adv. Appl. Prob. 6, 711731.
[2] De Meyer, A. (1982) On a theorem of Bingham and Doney. J. Appl. Prob. 19, 217220.
[3] De Meyer, A. and Teugels, J. L. (1980) On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1. J. Appl. Prob. 17, 802813.
[4] Evans, L. S. (1978) An upper bound for the mean of Yaglom's limit. J. Appl. Prob. 15, 199201.
[5] Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.
[6] Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.
[7] Yaglom, A. M. (1947) Certain limit theorems of the theory of branching random processes (in Russian). Soviet Math. Dokl. 56, 795798.

Keywords

Asymptotic properties of subcritical Galton-Watson processes

  • J. H. Bagley (a1)

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