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

Author

Listed:
  • Stéphane Chrétien

    (National Physical Laboratory, Hampton Road, Teddinton TW11 0LW, UK)

  • Juan-Pablo Ortega

    (Faculty of Mathematics and Statistics, University of St. Gallen, CH-9000 St. Gallen, Switzerland)

Abstract

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.

Suggested Citation

  • Stéphane Chrétien & Juan-Pablo Ortega, 2018. "A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone," Mathematics, MDPI, vol. 6(3), pages 1-5, March.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:3:p:35-:d:134355
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    References listed on IDEAS

    as
    1. T. Duncan & B. Pasik-Duncan & L. Stettner, 2005. "Ergodic and adaptive control of hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 297-318, November.
    2. Elon Kohlberg & John W. Pratt, 1982. "The Contraction Mapping Approach to the Perron-Frobenius Theory: Why Hilbert's Metric?," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 198-210, May.
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