On the stationary distribution of some extremal Markovian sequences

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.