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2011 Moments of recurrence times for Markov chains
Frank Aurzada, Hanna Döring, Marcel Ortgiese, Michael Scheutzow
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Electron. Commun. Probab. 16: 296-303 (2011). DOI: 10.1214/ECP.v16-1632


We consider moments of the return times (or first hitting times) in an irreducible discrete time discrete space Markov chain. It is classical that the finiteness of the first moment of a return time of one state implies the finiteness of the first moment of the first return time of any other state. We extend this statement to moments with respect to a function $f$, where $f$ satisfies a certain, best possible condition. This generalizes results of K.L. Chung (1954) who considered the functions $f(n)=n^p$ and wondered "[...] what property of the power $n^p$ lies behind this theorem [...]" (see Chung (1967), p. 70). We exhibit that exactly the functions that do not increase exponentially - neither globally nor locally - fulfill the above statement.


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Frank Aurzada. Hanna Döring. Marcel Ortgiese. Michael Scheutzow. "Moments of recurrence times for Markov chains." Electron. Commun. Probab. 16 296 - 303, 2011.


Accepted: 8 June 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1231.60063
MathSciNet: MR2811181
Digital Object Identifier: 10.1214/ECP.v16-1632

Primary: 60J10


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