Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distribution of the supremum for spectrally asymmetric L\'evy
  processes   In this article we derive formulas for the probability $P(\sup_{t\leq T}
X(t)>u)$ $T>0$ and $P(\sup_{t<\infty} X(t)>u)$ where $X$ is a spectrally
positive L\'evy process with infinite variation. The formulas are
generalizations of the well-known Tak\'acs formulas for stochastic processes
with non-negative and interchangeable increments. Moreover, we find the joint
distribution of $\inf_{t\leq T} Y(t)$ and $Y(T)$ where $Y$ is a spectrally
negative L\'evy process.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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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: solv-int
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph