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Analytical approximation to the multidimensional Fokker–Planck equation with steady state

Martin, R. J., Craster, R. V., Pannier, A. and Kearney, M. J. (2019) Analytical approximation to the multidimensional Fokker–Planck equation with steady state Journal of Physics A: Mathematical and Theoretical, 52, 085002.

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The Fokker–Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein–Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are 'far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences
Authors :
Martin, R. J.
Craster, R. V.
Pannier, A.
Kearney, M.
Date : 29 January 2019
Funders : Leverhulme Trust
DOI : 10.1088/1751-8121/aafea3
Copyright Disclaimer : Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Depositing User : Christine Daoutis
Date Deposited : 01 Mar 2019 12:32
Last Modified : 01 Mar 2019 12:32

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