Probabilistic characterization of nonlinear systems under Poisson white noise parametric input via complex fractional moments

In this paper the probabilistic characterization of a nonlinear system enforced by parametric Poissonian white noise in terms of complex fractional moments is presented. In fact the initial system driven by a parametric input could be transformed into a system with an external type of excitation through an invertible nonlinear transformation. It is shown that by using Mellin transform theorem and related concepts, the solution of the Kolmogorov-Feller equation for the system with external input may be obtained in a very easy way.