Linear systems with polynomials of filtered Poisson processes

Moment equations are calculated exactly for the response of linear systems subjected polynomials of filtered Poisson processes. The Itô formula for stochastic differential equations driven by Poisson white noise is applied to derive moment equations. It is shown that the set of moment equations is closed. The proposed method is used to calculate moments up to the fourth order for the response of two linear systems subjected to quadratic forms of filtered Poisson processes. Results by Monte Carlo simulations are also presented for comparison.