Response of Linear Systems to Polynomials of Gaussian Processes

Abstract

Moments and mean crossing rates are determined for the response of linear systems subject to polynomial forms in Gauss-Markov processes. Differential equations describing the evolution in time of response moments are developed by the use of Itô’s calculus. Estimators are obtained for mean crossing rates based on higher order moments and approximations of the distribution of the response. The method is applied to the analysis of a simple oscillator subject to the square of an Ornstein-Uhlenbeck process.