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.
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Bernadac, E. Random continued fractions and inverse Gaussian distribution on a symmetric cone. J Theor Probab 8, 221–259 (1995). https://doi.org/10.1007/BF02212879
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DOI: https://doi.org/10.1007/BF02212879