The Annals of Probability

Random continued fractions with beta-hypergeometric distribution

Gérard Letac and Mauro Piccioni

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In a recent paper [Statist. Probab. Lett. 78 (2008) 1711–1721] it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function 2F1. In the present paper we fully exploit a formula due to Thomae [J. Reine Angew. Math. 87 (1879) 26–73] in order to generalize substantially the class of random continuous fractions with a density of the above form. This involves the design of seven particular graphs. Infinite paths on them lead to random continued fractions with an explicit distribution. A careful study about the set of five real parameters leading to a beta-hypergeometric distribution is required, relying on almost forgotten results mainly due to Felix Klein.

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Ann. Probab., Volume 40, Number 3 (2012), 1105-1134.

First available in Project Euclid: 4 May 2012

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Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60E05: Distributions: general theory

Distributions on (0,1) with five parameters generalized hypergeometric functions periodic random continued fractions


Letac, Gérard; Piccioni, Mauro. Random continued fractions with beta-hypergeometric distribution. Ann. Probab. 40 (2012), no. 3, 1105--1134. doi:10.1214/10-AOP642.

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