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

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

2002-07-17

arxiv.org/abs/cond-mat/0207420v2

Phys. Rev. E 66, 041101 (2002)

Physics

Condensed Matter

Statistical Mechanics

A new ref.12 is added and discussed

Scientific paper

10.1103/PhysRevE.66.041101

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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