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Infinite product expansion of the Fokker-Planck equation with steady-state solution.

ABSTRACT: We present an analytical technique for solving Fokker-Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples.

SUBMITTER: Martin RJ

PROVIDER: S-EPMC4528656 | biostudies-literature | 2015 Jul

REPOSITORIES: biostudies-literature

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Infinite product expansion of the Fokker-Planck equation with steady-state solution.

Martin R J RJ Craster R V RV Kearney M J MJ

Proceedings. Mathematical, physical, and engineering sciences 20150701 2179

We present an analytical technique for solving Fokker-Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples. ...[more]

PMID: 26346100

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