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On the Stationary Distribution of Some Extremal Markovian Sequences

M. T. Alpuim and E. Athayde
Journal of Applied Probability
Vol. 27, No. 2 (Jun., 1990), pp. 291-302
DOI: 10.2307/3214648
Stable URL: http://www.jstor.org/stable/3214648
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Stationary Distribution of Some Extremal Markovian Sequences
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Abstract

This paper is concerned with the Markovian sequence Xn = Zn max{Xn-1, Yn}, n ≥ 1 where X0 is any random variable, {Zn} and {Yn} are independent sequences of i.i.d. random variables both independent of X0. We consider the problem of characterizing the class of stationary distributions arising in such a model and give criteria for a d.f. to belong to it. We develop further results when the Zn's are random variables concentrated on the interval [0,1], namely having a beta distribution.

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