Moment equations are calculated exactly for the response of linear sys
tems subjected polynomials of filtered Poisson processes. The Ito form
ula for stochastic differential equations driven by Poisson white nois
e is applied to derive moment equations. It is shown that the set of m
oment equations is closed. The proposed method is used to calculate mo
ments up to the fourth order for the response of two linear systems su
bjected td quadratic forms of filtered Poisson processes. Results by M
onte Carlo simulations are also presented for comparison. (C) 1997 Els
evier Science Ltd.