In this paper we consider an independent and identically distributed sequence {Yn} with common distribution function F(x) and a random variable X0, independent of the Yi's, and define a Markovian sequence {Xn} as Xi = X0, 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.

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.

No abstract

This paper is concerned with the Markovian sequence Xn = Zn max{Xn– 1, Yn },n ≧ 1, where X 0 is any random variable, {Zn } and {Yn } are independent sequences of i.i.d. random variables both independent of X 0. 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.

No abstract