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Variational Schemes in the Fokker-Planck Equation

T. Blum·A. J. McKane
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Abstract

We investigate variational methods for finding approximate solutions to the Fokker-Planck equation, especially in cases lacking detailed balance. These schemes fall into two classes: those in which a Hermitian operator is constructed from the (non-Hermitian) Fokker-Planck operator, and those which are based on soluble approximations to this operator. The various approaches are first tested on a simple quantum-mechanical problem and then applied to a toy Fokker-Planck equation. The problem of a particle moving in a potential and subject to external non-white noise is then investigated using the formalism developed earlier on in the paper.

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T. Blum, A. J. McKane. 1995-05-10. Variational Schemes in the Fokker-Planck Equation. https://doi.org/10.1088/0305-4470%2F29%2F9%2F003

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