Summary
We consider the first return time distributions for each state in a Markov chain and show that finiteness of entropy of these distributions is a class property for recurrent and transient classes.
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Klimko, E. M., Sucheston, Louis: On convergence of information in spaces with infinite invariant measure. Z. Wahrscheinlichkeitstheorie verw. Geb.10, 226–235 (1968).
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The work of the second author was supported in part by National Science Foundation Grant GP 7631.
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Klimko, E.M., Yackel, J. Entropy of first return partitions of a Markov chain. Z. Wahrscheinlichkeitstheorie verw Gebiete 14, 251–253 (1970). https://doi.org/10.1007/BF01111420
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DOI: https://doi.org/10.1007/BF01111420