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

TL;DR

This paper extends the concept of continued fractions to symmetric cones using a division algorithm and provides convergence criteria for non-ordinary random continued fractions related to beta distributions on symmetric cones.

Contribution

It introduces a new framework for random continued fractions on symmetric cones and establishes convergence criteria, broadening the understanding of these structures in probability theory.

Findings

Established convergence criteria for non-ordinary random continued fractions on symmetric cones.

Extended the definition of continued fractions to symmetric cones using a division algorithm.

Linked the convergence of these fractions to distributions related to the beta distribution on cones.

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.