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Ergodicity and mixing conditions of Markov processes in nonparametric filtering problems. (English. Russian original) Zbl 0753.93076
Autom. Remote Control 52, No. 4, 472-479 (1991); translation from Avtom. Telemekh. 1991, No. 4, 36-45 (1991).
The problem of filtering a discrete-time Markov process is considered in the case where the law of the state process is unknown; only the dependence between the state and the observation are known. The authors study ergodicity and strong mixing conditions for the system. Then, by applying a classical nonparametric estimator for the density, they can deduce nonparametric filters which are asymptotically optimal.
93E11 Filtering in stochastic control theory
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)