A random continued fraction in Rd+1 with an inverse Gaussian distribution

Letac, Gérard; Seshadri, Vanamamalai

Bernoulli, Tome 1 (1995) no. 3, p. 381-393 / Harvested from Project Euclid

Résumé

A continued fraction in R^d+1 is the composition of an infinite number of projectivities of R^d+1 which preserve (0,+∞)×R^d. We consider a right random walk on the semigroup of such projectivities governed by a special distribution, and we prove that the corresponding random continued fraction has a generalized inverse Gaussian distributionon R^d+1. This leads to a characterization of these distributions.

Publié le : 1995-12-14
Classification: characterizations, iteration of random functions, random walks on matrices

@article{1193758713,
     author = {Letac, G\'erard and Seshadri, Vanamamalai},
     title = {A random continued fraction in Rd+1 with an inverse Gaussian distribution},
     journal = {Bernoulli},
     volume = {1},
     number = {3},
     year = {1995},
     pages = { 381-393},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1193758713}
}

Letac, Gérard; Seshadri, Vanamamalai. A random continued fraction in Rd+1 with an inverse Gaussian distribution. Bernoulli, Tome 1 (1995) no. 3, pp.  381-393. http://gdmltest.u-ga.fr/item/1193758713/