Optimal Filtering: Volume I: Filtering of Stochastic Processes

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This work considers methods of optimal signal processing. The generalized filtering theory presented includes both highly developed, now classical branches like the Wiener-Kolmogorov and Kalman-Bucy theories, as well as relatively new branches such as semidegenerate processes and minimax filtering. The two-level approach to filtering problems is applied depending on their complexity. Starting with the conventional notions of filtering theory, in terms of difference-differential models, the research proceeds to notions and constructions of functional analysis convenient for analyzing linear filtering problems. Many novel results on filtering theory are also introduced. This volume should be of interest to experts in the design of signal processing and theorists in functional analysis, probability theory, and mathematical physics.