Limit theorems for the minimal position in a branching random walk with independent logconcave displacements
2000 ◽
Vol 32
(1)
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pp. 159-176
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Keyword(s):
Time Lag
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Consider a branching random walk in which each particle has a random number (one or more) of offspring particles that are displaced independently of each other according to a logconcave density. Under mild additional assumptions, we obtain the following results: the minimal position in the nth generation, adjusted by its α-quantile, converges weakly to a non-degenerate limiting distribution. There also exists a ‘conditional limit’ of the adjusted minimal position, which has a (Gumbel) extreme value distribution delayed by a random time-lag. Consequently, the unconditional limiting distribution is a mixture of extreme value distributions.
2000 ◽
Vol 32
(01)
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pp. 159-176
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1978 ◽
Vol 15
(03)
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pp. 639-644
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2013 ◽
Vol 28
(2)
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pp. 467-487
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1973 ◽
Vol 10
(01)
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pp. 39-53
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2014 ◽
Vol 34
(2)
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pp. 501-512
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Keyword(s):
2009 ◽
Vol 46
(1)
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pp. 61-96
2008 ◽
Vol DMTCS Proceedings vol. AI,...
(Proceedings)
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