On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex

Marc Peigne and Tat Dat Tran

Contact the author: Please use for correspondence this email.
Submission date: 03. Jun. 2020
Pages: 24
Bibtex
MSC-Numbers: 60J05, 60F05
Keywords and phrases: Iterated function systems, quasi-compact linear operators, absorbing compact set, invariant probability measure, invariant probability density
Download full preprint: PDF (805 kB)

Abstract:
In this paper, we give out a setting of an Diaconis and Freedman's chain in a multidimensional simplex and consider its asymptotic behavior. By using techniques in random iterated functions theory and quasi-compact operators theory, we first give out some sufficient conditions which ensure the existence and uniqueness of an invariant probability measure. In some particular cases, we give out explicit formulas of the invariant probability density. Moreover, we completely classify all behaviors of this chain in dimensional two. Eventually, some other settings of the chain are discussed.