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

Vadim A. Kaimanovich
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Vadim A. Kaimanovich: University of Edinburgh, Department of Mathematics

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 145-180 from Springer

Abstract: 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).

Keywords: Markov Chain; Probability Measure; Harmonic Function; Harmonic Measure; Path Space (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-1-4899-2323-3_13

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