Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solutions of a class of non-Markovian Fokker-Planck equations   We show that a formal solution of a rather general non-Markovian
Fokker-Planck equation can be represented in a form of an integral
decomposition and thus can be expressed through the solution of the Markovian
equation with the same Fokker-Planck operator. This allows us to classify
memory kernels into safe ones, for which the solution is always a probability
density, and dangerous ones, when this is not guaranteed. The first situation
describes random processes subordinated to a Wiener process, while the second
one typically corresponds to random processes showing a strong ballistic
component. In this case the non-Markovian Fokker-Planck equation is only valid
in a restricted range of parameters, initial and boundary conditions.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn