Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Martingale approach to subexponential asymptotics for random walks   Consider the random walk $S_n=\xi_1+...+\xi_n$ with independent and
identically distributed increments and negative mean $\mathbf E\xi=-m<0$. Let
$M=\sup_{0\le i} S_i$ be the supremum of the random walk. In this note we
present derivation of asymptotics for $\mathbf P(M>x), x\to\infty$ for
long-tailed distributions. This derivation is based on the martingale arguments
and does not require any prior knowledge of the theory of long-tailed
distributions. In addition the same approach allows to obtain asymptotics for
$\mathbf P(M_\tau>x)$, where $M_\tau=\max_{0\le i<\tau}S_i$ and
$\tau=\min\{n\ge 1: S_n\le 0 \}$.

1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th