Linear and nonlinear systems with non-Gaussian white noise input

Methods are examined for analyzing the response of linear and nonlinear systems subjected to two non-Gaussian white noise processes, the Poisson and the α-stable white noises. The analysis of linear systems is simple and can be based on the theory of filtered Poisson and α-stable random processes. On the other hand, there are no simple and efficient methods for the response analysis of nonlinear systems subjected to these non-Gaussian white noises. Several methods are presented and illustrated by examples. These methods include a Markov chain model with random time step, the Monte Carlo simulation, and extensions of the Itô calculus, the equivalent linearization, and the path integral techniques.