Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the strong Feller property of diffusion processes   In this note we prove the strong Feller property of a strong Markov quasi
diffusion process corresponding to an elliptic operator with merely bounded
measurable coefficients. We also prove H\"older continuity of harmonic
functions associated with the quasi diffusion process and Harnack inequality.
As an application, we show that for such diffusion processes the probabilistic
definition of a regular boundary point coincides with the 'analytic' one.
  The parabolic counterparts of these results are presented as well. The proofs
are adaptations of arguments from \cite{KrS_79} and \cite{Kr_18}.

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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc