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 ChamayouAffiliated withMatra, M.S.2I
  • , Gérard LetacAffiliated withLaboratoire de Statistique et Probabilités, Université Paul Sabatier-U.A. C.N.R.S. 745

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If (Y n) 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 (W n) n=0 defined byW n=Y nf(W n-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