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Moments of recurrence times for Markov chains


 
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1. Title Title of document Moments of recurrence times for Markov chains
 
2. Creator Author's name, affiliation, country Frank Aurzada; TU Berlin
 
2. Creator Author's name, affiliation, country Hanna Döring; TU Berlin
 
2. Creator Author's name, affiliation, country Marcel Ortgiese; TU Berlin
 
2. Creator Author's name, affiliation, country Michael Scheutzow; TU Berlin
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Discrete time Markov chain, recurrence time, generalized moment
 
3. Subject Subject classification 60J10
 
4. Description 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.
 
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7. Date (YYYY-MM-DD) 2011-06-08
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1632
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1632
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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