Path to survival for the critical branching processes in a random environment
2017 ◽
Vol 54
(2)
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pp. 588-602
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Keyword(s):
Abstract A critical branching process {Zk, k = 0, 1, 2, ...} in a random environment is considered. A conditional functional limit theorem for the properly scaled process {log Zpu, 0 ≤ u < ∞} is established under the assumptions that Zn > 0 and p ≪ n. It is shown that the limiting process is a Lévy process conditioned to stay nonnegative. The proof of this result is based on a limit theorem describing the distribution of the initial part of the trajectories of a driftless random walk conditioned to stay nonnegative.
2001 ◽
Vol 11
(6)
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Keyword(s):
2020 ◽
Vol 2020
(2)
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pp. 109-118
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2018 ◽
Vol 28
(1)
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pp. 7-22
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1998 ◽
Vol 30
(3)
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pp. 740-756
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Keyword(s):
1998 ◽
Vol 30
(03)
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pp. 740-756
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Keyword(s):
2019 ◽
Vol 29
(3)
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pp. 149-158
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Keyword(s):