A generalization of the Kalman filter to models with infinite variance

Alain Le Breton and Marek Musiela

Stochastic Processes and their Applications, 1993, vol. 47, issue 1, 75-94

Abstract: The 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.

Keywords: optimal linear filtering; prediction and smoothing semimartingales with infinite variance metric projection James' orthogonality left innovations (search for similar items in EconPapers)
Date: 1993
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