Dynamic Systems with Poisson White Noise

Methods are developed for finding properties of the output of linear and nonlinear dynamic systems to random actions represented by Poisson white noise and filtered Poisson processes. The Poisson white noise can be viewed as a sequence of independent, identically distributed pulses arriving at random times. The filtered Poisson process is the output of a linear filter to Poisson white noise. Three methods are considered for finding output properties. If the input has infrequent or frequent pulses, output properties can be obtained from a Markov model or the assumption that the input is a Gaussian white noise, respectively. Otherwise, a method based on Itô's formula for semimartingales is used to find output properties. Examples are used to illustrate the proposed methods.