The paper considers an independent and identically distributed sequence {Yn} with common distribution function F(x) and a random variable X0, independent of the Yi’s, and defines a Markovian sequence {Xn} as Xi=x0, if i=0, Xi=kmax{XiÅ-1,Yi}, if i≥1, k∈ℝ, 0∈k∈1. For this sequence it evaluates basic distributional formulas and gives conditions on F(x) for the sequence to possess a stationary distribution. The paper proves that for any distribution function H(x) with left endpoint greater than or equal to zero for which logH(ex) is concave it is possible to construct such a stationary sequence with marginal distributions equal to it. It studies the limit laws for extremes and kth order statistics.
