A METHOD FOR ESTIMATING INTENSITY AND IMPULSE-RESPONSE FUNCTIONS OF FILTERED POISSON PROCESSES

This paper presents a method for estimating the intensity and impulse response (IR) function of filtered Poisson processes, The case is cons idered where the filtered Poisson process is modeled as an output of t he linear constant-coefficient ordinary differential equations having poles and zeros driven by Poisson impulse processes, It is shown that an explicit formula for estimating the intensity is derived by combini ng second- and third-order cumulants of the residual time series gener ated from the discretized filtered Poisson process, It is also shown t hat the IR function can be estimated from the parameters of the discre tized filtered Poisson process, Then, Monte Carlo simulations demonstr ate the validity of the proposed method in some specific examples, It is concluded that the proposed method can be extensively applied to ac tual phenomena appearing in engineering and science.