Abstract
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.
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