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On solutions of a class of non-Markovian Fokker-Planck equations

I. M. Sokolov
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Abstract

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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I. M. Sokolov. 2002-07-29. On solutions of a class of non-Markovian Fokker-Planck equations. https://doi.org/10.1103/physreve.66.041101

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