Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments of recurrence times for Markov chains   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.

31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th