Direct derivation of response moment and cumulant equations for non-linearstochastic problems

A relatively straightforward formulation is presented for deriving the diff erential equations governing the evolution of the response moments and cumu lants of a dynamical system. This is a very general framework that applies to linear and non-linear systems subjected to external and multiplicative n on-Gaussian, delta-correlated processes. This formulation provides an alter native to both the partial differential Fokker-Planck equation that has som etimes been used in deriving moment or cumulant equations, and the differen tial (as opposed to derivative) relationships of the Ito calculus. It is be lieved that many analysts may find the technique used here to be more obvio us than the alternatives, since the derivative relationships for the stocha stic process are of the same form as in the more familiar ordinary differen tial equations, (C) 2000 Elsevier Science Ltd. All rights reserved.