Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic
  Equations   We study the stochastic solution to a Cauchy problem for a degenerate
parabolic equation arising from option pricing. When the diffusion coefficient
of the underlying price process is locally H\"older continuous with exponent
$\delta\in (0, 1]$, the stochastic solution, which represents the price of a
European option, is shown to be a classical solution to the Cauchy problem.
This improves the standard requirement $\delta\ge 1/2$. Uniqueness results,
including a Feynman-Kac formula and a comparison theorem, are established
without assuming the usual linear growth condition on the diffusion
coefficient. When the stochastic solution is not smooth, it is characterized as
the limit of an approximating smooth stochastic solutions. In deriving the main
results, we discover a new, probabilistic proof of Kotani's criterion for
martingality of a one-dimensional diffusion in natural scale.

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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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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: plasm-ph