Criteria of convergence of a non ordinary random continued fractions on a symmetric cone

Abstract

In this paper, we use a notion of ratio based on a division algorithm, to extend to a symmetric cone the definition of a continued fraction in its more general form. We then give a criteria of convergence of a non ordinary random continued fraction that has arisen in the study of some probability distributions related to the beta distribution on the cone of positive definite symmetric matrices or on any symmetric cone.