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.
RANDOM CONTINUED FRACTIONS WITH BETA-HYPERGEOMETRIC DISTRIBUTION / Gérard, Letac; Piccioni, Mauro. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - STAMPA. - 40:3(2012), pp. 1105-1134. [10.1214/10-aop642]
RANDOM CONTINUED FRACTIONS WITH BETA-HYPERGEOMETRIC DISTRIBUTION
PICCIONI, MAURO
2012
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
