Explicit stationary distributions for compositions of random functions and products of random matrices (Q805044)

The authors construct explicit examples of stationary distributions for the Markov chain \((W_ n)\) defined by \(W_ n=Y_ nf(W_{n-1})\), where \((Y_ n)\) is a sequence of i.i.d. random variables on (0,\(\infty)\) and f is a positive function on (0,\(\infty)\). Use of beta distributions of the first and second kind along with general exponential families on (0,\(\infty)\) has been made in constructing the examples. This model leads to interesting random continued fractions when f is a Möbius function.