Affordable Access

Moments of recurrence times for Markov chains

Authors
Type
Published Article
Publication Date
Submission Date
Source
arXiv
External links

Abstract

We consider moments of the return times (or first hitting times) in a 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.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments
F