A limit theorem for the maxima of the para-critical simple branching process
1998 ◽
Vol 30
(3)
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pp. 740-756
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Keyword(s):
Let Mn denote the size of the largest amongst the first n generations of a simple branching process. It is shown for near critical processes with a finite offspring variance that the law of Mn/n, conditioned on no extinction at or before n, has a non-defective weak limit. The proof uses a conditioned functional limit theorem deriving from the Feller-Lindvall (CB) diffusion limit for branching processes descended from increasing numbers of ancestors. Subsidiary results are given about hitting time laws for CB diffusions and Bessel processes.
1998 ◽
Vol 30
(03)
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pp. 740-756
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Keyword(s):
2017 ◽
Vol 54
(2)
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pp. 588-602
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Keyword(s):
2020 ◽
Vol 2020
(2)
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pp. 109-118
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2001 ◽
Vol 11
(6)
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Keyword(s):