Minimum error dispersion linear filtering of scalar symmetric stable processes

Abstract

The well-known Kalman-Bucy linear-filtering theory for Gaussian Markov processes is generalized to cover a particular class of non-Gaussian Markov processes, the scalar symmetric stable Markov processes. Results are presented only for discrete time because of certain pathologies that arise in the continuous-time analog (except in the Gaussian case). Attention is confined to the scalar case because of technical problems arising in characterizing multivariate stable distributions (except in the Gaussian case).