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

Abstract

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.