Inverse Mellin Transform to characterize the nonlinear system PDF response to Poisson white noise

In this paper the probabilistic characterization of nonlinear systems driven by Poissonian white noise is treated. Solution is pursued in terms of complex fractional moments and Mellin Transform. The main advantage in using such quantities, instead of the integer moments, relies on the fact that, through the complex fractional moments and the inverse Mellin transform, the probability density function is restituted in the whole domain with exception of the value in zero, in which singularities appear. It is shown that by using Mellin transform theorem and related concepts, the solution of the Kolmogorov-Feller equation is obtained in a very easy way by solving a set of linear differential equations. Results are compared with those of Monte Carlo Simulation showing the robustness of the solution pursued in terms of Complex fractional moments. Further a very elegant strategy to give a relationship between the Complex fractional moments evaluated for different value of real part is introduced as well.