Higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses

The higher order statistics of the response of linear systems excited by po lynomials of filtered Poisson pulses are evaluated by means of knowledge of the first order statistics and without any further integration. This is ma de possible by a coordinate transformation which replaces the original syst em by a quasi-linear one with parametric Poisson delta-correlated input; an d, for these systems, a simple relationship between first order and higher order statistics is found in which the transition matrix of the dynamical n ew system, incremented by the correction terms necessary to apply the Ita c alculus, appears. (C) 1998 Elsevier Science Ltd. All rights reserved.