Detection-filter representations for Markov jump diffusions

The problem considered is filtering for Gaussian observations of linear differential systems that are driven by both Wiener processes and marked Poisson point processes. Well-known representations of the MMSE-filter for such a Markov jump-diffusion are a differential for the evolution of its conditional density or differentials for all its...

On martingales and recursive optimal state estimation

This report constitutes the deposit of a study of literature on martingales and estimation theory. Some experimental work concerning the efficiency of an estimation algorithm based on martingales is also described. The investigation has been guided by the intent to investigate martingales in relation to the Kalman and Kalman-Bucy filters and to...