Some reflections on the efficacy of moment closure methods

摘要

In the process of attempting to verify statistical moments of response for nonlinear stochastic systems obtained through the numerical solution of the Fokker-Planck equation, the authors observed significant discrepancies between their results and those obtained through direct solution of moment equations employing various closure schemes. Further investigation has led to the examination of the convergence properties of those methods, and some results of that effort are reported herein.