Journal of Theoretical Probability

, Volume 4, Issue 1, pp 3–36

Explicit stationary distributions for compositions of random functions and products of random matrices

  • Jean-François Chamayou
  • Gérard Letac
Article

DOI: 10.1007/BF01046992

Cite this article as:
Chamayou, JF. & Letac, G. J Theor Probab (1991) 4: 3. doi:10.1007/BF01046992

Abstract

If (Yn)n=1/∞ is a sequence of i.i.d. random variables onE=(0,+∞) and iff is positive onE, this paper studies explicit examples of stationary distributions for the Markov chain (Wn)n=0 defined byWn=Ynf(Wn-1). The case wheref is a Moebius function(ax+b)/(cx+d) leads to products of certain random (2,2) matrices and to interesting random continued fractions. These explicit examples are built with a naive idea by considering genral exponential families onE, especially the families of beta distributions of the first and second kind.

Key Words

Random matrices random walks inGL(2,ℝ) beta and hypergeometric distributions exponential families 

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Jean-François Chamayou
    • 1
  • Gérard Letac
    • 2
  1. 1.Matra, M.S.2IToulouseFrance
  2. 2.Laboratoire de Statistique et ProbabilitésUniversité Paul Sabatier-U.A. C.N.R.S. 745Toulouse CedexFrance