Abstract
If (Y n) =1/∞ n 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.
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Chamayou, JF., Letac, G. Explicit stationary distributions for compositions of random functions and products of random matrices. J Theor Probab 4, 3–36 (1991). https://doi.org/10.1007/BF01046992
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DOI: https://doi.org/10.1007/BF01046992