Stochastic Filtration for Moving Intensity of Poisson Flow with Random Jumps at Random Moments

Abstract

A wide range of events in Queuing networks, stock exchanges, and automatic systems can be described by a Poisson flow model with changing intensity that undergoes random jumps at a priori unknown moments. The direct solution of the identification problem in such conditions leads to algorithms with exponential complexity. An asymptotically optimal ML filtering algorithm for observed Poisson flow with polynomial computational complexity is proposed. It is shown that the optimal estimates of the moments of jumps must coincide with one of the moments of the observed events.