Abstract
Boundary theory for recurrent chains proceeds along altogether different lines from the approach in Chapter 10. A clue to the difficulty is that every non-negative superregular function is constant, and hence the representation of such functions degenerates. Moreover, since a recurrent chain is in every state infinitely often with probability one, an almost-everywhere convergence theorem is out of the question.
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© 1976 Springer-Verlag New York Inc.
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Kemeny, J.G., Snell, J.L., Knapp, A.W. (1976). Recurrent Boundary Theory. In: Denumerable Markov Chains. Graduate Texts in Mathematics, vol 40. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9455-6_11
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DOI: https://doi.org/10.1007/978-1-4684-9455-6_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9457-0
Online ISBN: 978-1-4684-9455-6
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