Random continued fractions and inverse Gaussian distribution on a symmetric cone
- Cite this article as:
- Bernadac, E. J Theor Probab (1995) 8: 221. doi:10.1007/BF02212879
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In this paper we introduce the inverse Gaussian and Wishart distributions on the cone of real (n, n) symmetric positive definite matricesHn+(ℝ) and more generally on an irreducible symmetric coneC. Then we study the convergence of random continued fractions onHn+(ℝ) andC by means of real Lagrangians forHn+(ℝ) and by new algebraic identities on symmetric cones forC. Finally we get a characterization of the inverse Gaussian distribution onHn+(ℝ) andC.