Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harnack Inequalities for Degenerate Diffusions   We study various probabilistic and analytical properties of a class of
degenerate diffusion operators arising in Population Genetics, the so-called
generalized Kimura diffusion operators. Our main results is a stochastic
representation of weak solutions to a degenerate parabolic equation with
singular lower-order coefficients, and the proof of the scale-invariant Harnack
inequality for nonnegative solutions to the Kimura parabolic equation. The
stochastic representation of solutions that we establish is a considerable
generalization of the classical results on Feynman-Kac formulas concerning the
assumptions on the degeneracy of the diffusion matrix, the boundedness of the
drift coefficients, and on the a priori regularity of the weak solutions.

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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: stat