Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic functions and stationary distributions for asymptotically
  homogeneous transition kernels on $Z^+$   We suggest a method for constructing positive harmonic functions for a wide
class of transition kernels on $Z^+$. We also find natural conditions under
which these functions have positive finite limits at infinity. Further, we
apply our results on harmonic functions to asymptotically homogeneous Markov
chains on $Z^+$ with asymptotically negative drift. More precisely, assuming
that Markov chain satisfy Cram\'er's condition, we study the tail asymptotics
of the stationary distribution. In particular, we clarify the influence of the
rate of convergence of jumps of the chain towards the limiting distribution.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an