A continued fraction in Rd+1 is the composition of an infinite number of projectivities of Rd+1 which preserve (0,+∞)×Rd. 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 Rd+1. This leads to a characterization of these distributions.
"A random continued fraction in Rd+1 with an inverse Gaussian distribution." Bernoulli 1 (4) 381 - 393, December 1995. https://doi.org/10.3150/bj/1193758713