Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schroedinger's interpolation problem and its probabilistic solutions   Probablistic solutions of the so called Schr\"{o}dinger boundary data problem
provide for a unique Markovian interpolation between any two strictly positive
probability densities designed to form the input-output statistics data for a
certain dynamical process taking place in a finite-time interval. The key
problem is to select the jointly continuous in all variables positive semigroup
kernel, appropriate for the phenomenological (physical) situation.

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The categories of this paper are: cs
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys