An extremal markovian sequence
1989 ◽
Vol 26
(02)
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pp. 219-232
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Keyword(s):
In this paper we consider an independent and identically distributed sequence {Yn } with common distribution function F(x) and a random variable X 0, independent of the Yi 's, and define a Markovian sequence {Xn } as Xi = X 0, if i = 0, Xi = k max{Xi − 1, Yi }, if i ≧ 1, k ∈ R, 0 < k < 1. For this sequence we evaluate basic distributional formulas and give conditions on F(x) for the sequence to possess a stationary distribution. We prove that for any distribution function H(x) with left endpoint greater than or equal to zero for which log H(ex ) is concave it is possible to construct such a stationary sequence with marginal distributions equal to it. We study the limit laws for extremes and kth order statistics.
1987 ◽
Vol 102
(2)
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pp. 329-349
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2016 ◽
Vol 31
(3)
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pp. 366-380
1995 ◽
Vol 118
(2)
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pp. 375-382
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2013 ◽
Vol 28
(2)
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pp. 209-222
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2005 ◽
Vol 127
(1)
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pp. 1767-1783
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2011 ◽
Vol 48
(01)
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pp. 238-257
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