Estimation of the Rate of a Discrete-Time Multivariate Point Process.

Abstract

We introduce the notion of a discrete-time multivariate point process which can arise in the modeling of an optical communication system. We wish to estimate the rate of this process at time t given the past of the process up to time t-l. This requires the computation of a certain conditional expectation: we perform this computation by introducing an absolutely continuous change of measure and then applying the generalized Bayes' rule.