A generalization of the Kalman filter to models with infinite variance

AbstractThe problem of optimal linear estimation for continuous time processes is investigated. The signal and observation processes are solutions of a linear system. The optimal filter is given by recursive equations which reduce to the classical Kalman-Bucy equations when the system is driven by independent white noises. The filter is defined by a left innovations process. Solutions to the prediction and smoothing problems are obtained. The assumptions concerning the errors allow to consider models with infinite variance