@article{ECP1632,
author = {Frank Aurzada and Hanna Döring and Marcel Ortgiese and Michael Scheutzow},
title = {Moments of recurrence times for Markov chains},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {16},
year = {2011},
keywords = {Discrete time Markov chain, recurrence time, generalized moment},
abstract = {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.},
pages = {no. 28, 296-303},
issn = {1083-589X},
doi = {10.1214/ECP.v16-1632},
url = {http://ecp.ejpecp.org/article/view/1632}}