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On the stationary distribution of some extremal Markovian sequences

Published online by Cambridge University Press:  14 July 2016

M. T. Alpuim  and
E. Athayde
M. T. Alpuim
Affiliation:
University of Lisbon and CEA (INIC)
E. Athayde*
Affiliation:
University of Lisbon and CEA (INIC)
*
∗Postal address for both authors: DEIOC, University of Lisbon, 58 Rua da Escola Politécnica, 1294 Lisboa Codex, Portugal.
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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.

Keywords

LIMIT DISTRIBUTIONBETA DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 291 - 302
Copyright
Copyright © Applied Probability Trust 1990 

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