Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Key Renewal Theorem for a Transient Markov Chain   We consider a time-homogeneous Markov chain $X_n$, $n\ge0$, valued in ${\bf
R}$. Suppose that this chain is transient, that is, $X_n$ generates a
$\sigma$-finite renewal measure. We prove the key renewal theorem under
condition that this chain has asymptotically homogeneous at infinity jumps and
asymptotically positive drift.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th