RANDOM CONTINUED FRACTIONS WITH BETA-HYPERGEOMETRIC DISTRIBUTION

• 成果类型: Article
• 署名作者: Letac, Gerard; Piccioni, Mauro
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sapienza University Rome
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP642
• 发表日期: 2012
• 页码: 1105-1134
• 关键词: series

摘要

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 F-2(1). 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.