Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper and Lower Bounds in Exponential Tauberian Theorems   In this text we study, for positive random variables, the relation between
the behaviour of the Laplace transform near infinity and the distribution near
zero. A result of De Bruijn shows that $E(e^{-\lambda X}) \sim
\exp(r\lambda^\alpha)$ for $\lambda\to\infty$ and $P(X\leq\epsilon) \sim
\exp(s/\epsilon^\beta)$ for $\epsilon\downarrow0$ are in some sense equivalent
(for $1/\alpha = 1/\beta + 1$) and gives a relation between the constants $r$
and $s$. We illustrate how this result can be used to obtain simple large
deviation results. For use in more complex situations we also give a
generalisation of De Bruijn's result to the case when the upper and lower
limits are different from each other.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas