The exponential rate of convergence of the distribution of the maximum of a random walk. Part II
Keyword(s):
The Real
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Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn (x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G ∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].
1975 ◽
Vol 12
(02)
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pp. 279-288
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1982 ◽
Vol 18
(4)
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pp. 343-348
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Keyword(s):
2014 ◽
1991 ◽
Vol 35
(2)
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pp. 79-91
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1984 ◽
Vol 2
(3)
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pp. 139-142
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