Linear systems excited by polynomial forms of non-Gaussian filtered processes

A method for the evaluation of the statistical moments of linear one-dimensional or multi-dimensional systems subjected to non-Gaussian input in polynomial forms of filtered normal or non-normal delta-correlated processes is presented. The proposed procedure allows one to avoid the solution of a set of non-linear differential equations, requiring the solution of three sets of linear differential equations. The latter sets are: the equations governing the evolution of the moments of the response forced by input-output cross moments; the equations useful for the evaluation of the input-output cross-moments and the equations governing the evolution of the statistical moments of the filtered input.