A Method of Self-Consistent Approximation for the Evolution Equation of a Probability Distribution

Abstract

A self-consistent approximation method for an evolution equation of a probability distribution which is not far from Gaussian is proposed by using an information-theoretical quantity, that is, Kullback-Leibler’s information. One typical example is considered as an illustration. It is also shown that the results are concisely represented by the Wiener-Hermite expansion.