Explicit stationary distributions for compositions of random functions and products of random matrices
- Cite this article as:
- Chamayou, JF. & Letac, G. J Theor Probab (1991) 4: 3. doi:10.1007/BF01046992
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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.