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

Abstract

A path-integral solution is derived for processes described by nonlinear Fokker-Planck 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 shown to give accurate results.