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Measure-Theoretic Boundaries of Markov Chains, 0–2 Laws and Entropy

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Harmonic Analysis and Discrete Potential Theory

Abstract

The classic Poisson formula giving an integral representation of bounded harmonic functions in the unit disk in terms of its boundary values has a long history (as it follows from its very name). Given a Markov operator P on a state space X one can easily define harmonic functions as invariant functions of the operator P, but in order to speak about their boundary values one needs a boundary, because no boundary is normally attached to the state space of a Markov chain (as distinct from bounded Euclidean domains common for the classic potential theory).

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Edinburgh, Edinburgh, Scotland

    Vadim A. Kaimanovich

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  1. Vadim A. Kaimanovich
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Editors and Affiliations

  1. University of Rome “Tor Vergata”, Rome, Italy

    Massimo A. Picardello

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© 1992 Springer Science+Business Media New York

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Kaimanovich, V.A. (1992). Measure-Theoretic Boundaries of Markov Chains, 0–2 Laws and Entropy. In: Picardello, M.A. (eds) Harmonic Analysis and Discrete Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2323-3_13

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  • DOI: https://doi.org/10.1007/978-1-4899-2323-3_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-2325-7

  • Online ISBN: 978-1-4899-2323-3

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