Nonlinear systems driven by polynomials of filtered Poisson processes

The perturbation method is applied to determine approximately the mean, variance, skewness and kurtosis of the transient and stationary response of nonlinear systems driven by polynomials of filtered Poisson processes. The analysis is based on the classical perturbation method, the Itô differentiation formula, and properties of the response of linear systems subjected to polynomials of filtered Poisson processes. Two examples are presented to demostrate the efficiency and accuracy of this approximate analysis.