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A Random Continued Fraction in Rd+1 with an Inverse Gaussian Distribution
Gérard Letac and Vanamamalai Seshadri
Vol. 1, No. 4 (Dec., 1995), pp. 381-393
Published by: International Statistical Institute (ISI) and the Bernoulli Society for Mathematical Statistics and Probability
Stable URL: http://www.jstor.org/stable/3318490
Page Count: 13
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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 distribution on Rd+1. This leads to a characterization of these distributions.
Bernoulli © 1995 Bernoulli Society for Mathematical Statistics and Probability