A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-c...

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Bibliographic Details
Published inMathematics (Basel) Vol. 6; no. 3; p. 35
Main Authors Chrétien, Stéphane, Ortega, Juan-Pablo
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 02.03.2018
Subjects
dynamical systems
Hilbert metric
Liverani’s formula
Markov processes
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Summary:The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-compact and multidimensional setting with a different cone, taylored for sub-Gaussian tails.
ISSN:2227-7390
2227-7390
DOI:10.3390/math6030035