Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ladder epochs and ladder chain of a Markov random walk with discrete
  driving chain   Let $(M_{n},S_{n})_{n\ge 0}$ be a Markov random walk with positive recurrent
driving chain $(M_{n})_{n\ge 0}$ having countable state space $\mathcal{S}$ and
stationary distribution $\pi$. It is shown in this note that, if the dual
sequence $({}^{\#}M_{n},{}^{\#}S_{n})_{n\ge 0}$ is positive divergent, i.e.
${}^{\#}S_{n}\to\infty$ a.s., then the strictly ascending ladder epochs
$\sigma_{n}^{>}$ of $(M_{n},S_{n})_{n\ge 0}$ are a.s. finite and the ladder
chain $(M_{\sigma_{n}^{>}})_{n\ge 0}$ is positive recurrent on some
$\mathcal{S}^{>}\subset\mathcal{S}$. We also provide simple expressions for its
stationary distribution $\pi^{>}$, an extension of the result to the case when
$(M_{n})_{n\ge 0}$ is null recurrent, and a counterexample that demonstrates
that ${}^{\#}S_{n}\to\infty$ a.s. does not necessarily entail $S_{n}\to\infty$
a.s., but rather $\limsup_{n\to\infty}S_{n}=\infty$ a.s. only. Our arguments
are based on Palm duality theory, coupling and the Wiener-Hopf factorization
for Markov random walks with discrete driving chain.

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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: physics