The Critical Galton-Watson Process Without Further Power Moments
2007 ◽
Vol 44
(03)
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pp. 753-769
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Keyword(s):
In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process {Z n ; n ≥ 0} with offspring generating function s + (1 − s)L((1 − s)−1), where L(x) is slowly varying. In contrast to a well-known theorem of Slack (1968), (1972) we use a functional normalization, which gives an exponential limit. We also give an alternative proof of Sze's (1976) result on the asymptotic behavior of the nonextinction probability.
2007 ◽
Vol 44
(3)
◽
pp. 753-769
◽
1987 ◽
Vol 15
(3)
◽
pp. 1052-1061
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Keyword(s):
1995 ◽
Vol 186
(3)
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pp. 371-389
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2003 ◽
Vol 43
(3)
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pp. 567-583
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1971 ◽
Vol 8
(03)
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pp. 589-598
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