A Random Difference Equation with Dufresne Variables revisited
Abstract
The Dufresne laws (laws of product of independent random variables with gamma and beta distributions) occur as stationary distribution of certain Markov chains Xn on R defined by: equation Xn = An ( Xn-1 + Bn ) equation where X0 , (A1,B1),...,(An,Bn) are independent and the (Ai,Bi)'s are identically distributed. This paper generalizes an explicit example where A is the product of two independent βa,1 , βb,1 and B γ1 or γ2 . Keywords: beta, gamma and Dufresne distributions,Markov chains, stationary distributions, hypergeometric differential equations, Poisson process.
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