On the Smoothing Estimation Problem for the Intensity of a DSMPP

The smoothing estimation problem for the intensity process of a doubly stochastic multichannel Poisson process is investigated. Recursive procedures for the efficient computation of the fixed-point as well as the fixed-interval smoothing estimators of the intensity process are designed. The only hypothesis imposed is that the covariance function of the intensity process is finite-dimensional and known. Thus, the provided solution is valid for both stationary and non-stationary processes.