Expansion for the moments of a nonlinear stochastic model

Abstract

We present a procedure to systematically evaluate all the moments of the Fokker-Planck equation by expanding them in a power series in a given function of t. The expansion coefficients are easily determined in terms of algebraic recursion relations. Applications to a linear Fokker-Planck equation, as well as to a truly nonlinear mean-field model, whose drift coefficient exhibits a functional dependence on the distribution function, show this formalism to be advantageous over the standard time series expansion of the moments which is shown to be rather impractical.