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On Distribution Tails and Expectations of Maxima in Critical Branching Processes
K. A. Borovkov and V. A. Vatutin
Journal of Applied Probability
Vol. 33, No. 3 (Sep., 1996), pp. 614-622
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215343
Page Count: 9
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We derive the limit behaviour of the distribution tail of the global maximum of a critical Galton-Watson process and also of the expectations of partial maxima of the process, when the offspring law belongs to the domain of attraction of a stable law. Thus the Lindvall (1976) and Athreya (1988) results are extended to the infinite variance case. It is shown that in the general case these two asymptotics are closely related to each other, and the latter follows readily from the former. We also discuss a related problem from the theory of general branching processes.
Journal of Applied Probability © 1996 Applied Probability Trust