Minimax a posteriori estimation of the Markov processes with finite state spaces

Abstract

Consideration was given to some problems of estimation (filtering and identification) in the observation systems describing the Markov processes with finite state spaces. The transition intensity matrices and the observation plan are random and have unknown distributions of some class. The conditional expectations of the accessible observations of some quadratic functions of the estimate errors are used as the performance criteria. The estimation problems under study lie in constructing estimates minimizing the conditional mean losses corresponding to the least favorable distribution of the “transition intensity matrix-observation plan matrix” pair from the set of permissible distributions. For the corresponding minimax problems, existence of the saddle points was proved, and the form of the corresponding minimax estimates was established.