Numerical evaluation of path-integral solutions to Fokker-Planck equations. II: Restricted stochastic processes

A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a...

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Bibliographic Details
Published in:Physical review. A, General physics General physics, 1983-11, Vol.28 (5), p.3003-3011
Main Authors: WEHNER, M. F, WOLFER, W. G
Format: Article
Language:English
Subjects:
657000 - Theoretical & Mathematical Physics
990200 - Mathematics & Computers
BOUNDARY CONDITIONS
CALCULATION METHODS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
FOKKER-PLANCK EQUATION
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
NUMERICAL ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
STOCHASTIC PROCESSES
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Summary:A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs.
ISSN:0556-2791
DOI:10.1103/PhysRevA.28.3003