Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An old efficient approach to anomalous Brownian motion   A number of random processes in various fields of science is described by
phenomenological equations containing a stochastic force, the best known
example being the Langevin equation (LE) for the Brownian motion (BM) of
particles. Long ago Vladimirsky (1942) proposed a simple method for solving
such equations. The method, based on the classical Gibbs statistics, consists
in converting the stochastic LE into a deterministic one, and is applicable to
linear equations with any kind of memory. When the memory effects are taken
into account in the description of the BM, the mean square displacement of the
particle at long times can exhibit an "anomalous" (different from that in the
Einstein theory) time dependence. In the present paper we show how some general
properties of such anomalous BM can be easily derived using the Vladimirsky
approach. The method can be effectively used in solving many of the problems
currently considered in the literature. We apply it to the description of the
BM when the memory kernel in the Volterra-type integro-differential LE
exponentially decreases with the time. The problem of the hydrodynamic BM of a
charged particle in an external magnetic field is also solved.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph