Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A renewal theorem and supremum of a perturbed random walk   We study tails of the supremum of a perturbed random walk under regime which
was not yet considered in the literature. Our approach is based on a new
renewal theorem, which is of independent interest. We obtain first and second
order asymptotics of the solution to renewal equation under weak assumptions
and we apply these results to obtain first and second order asymptotics of the
tail of the supremum of a perturbed random walk.

10
The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics