Abstract
We generalize Quine's result on the convergence of the extinction probability of the supercritical Galton-Watson process to one if the average number of offsprings tends to one without any restrictions on factorial moments.
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References
I. I. Gikhman and A. V. Skorokhod,Theory of Random Processes [in Russian], Vol. 2, Nauka, Moscow (1973).
B. A. Sevast'yanov,Branching Processes [in Russian], Nauka, Moscow (1971).
M. P. Quine, “Bounds for the extinction probability of a simple branching process,”J. Appl. Probab.,13, No. 1, 9–16 (1976).
V. V. Goryainov, “Fractional iteration of generating probability functions and imbedding of discrete branching processes in continuous ones,”Mat. Sb.,184, No. 5, 55–74 (1993).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 290–291, February, 1995.
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Goryainov, V.V. Estimates of the extinction probability of the Galton-Watson process. Ukr Math J 47, 341–343 (1995). https://doi.org/10.1007/BF01056724
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DOI: https://doi.org/10.1007/BF01056724