, Volume 8, Issue 2, pp 221-259

Random continued fractions and inverse Gaussian distribution on a symmetric cone

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Abstract

In this paper we introduce the inverse Gaussian and Wishart distributions on the cone of real (n, n) symmetric positive definite matricesH n + (ℝ) and more generally on an irreducible symmetric coneC. Then we study the convergence of random continued fractions onH n + (ℝ) andC by means of real Lagrangians forH n + (ℝ) and by new algebraic identities on symmetric cones forC. Finally we get a characterization of the inverse Gaussian distribution onH n + (ℝ) andC.