Controllable Markov Jump Processes. I. Optimum Filtering Based on Complex Observationsстатья
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Дата последнего поиска статьи во внешних источниках: 10 октября 2019 г.
Авторы:Borisov A.V.,
Miller G.B.,
Stefanovich A.I.
Аннотация:The first part of the paper is devoted to justifying the possibility of the correct description of a controllable stochastic observation system. The state is a Markov jump process, and the observations are a combination of continuous, discrete, and counting processes. A martingale problem of the system under study is solved: it is shown that there exists a canonical probability space with filtration such that under any admissible control, this system is stochastic differential with the martingales on the right-hand side. Further, for this system there exists a solution of the optimal in the mean square sense filtering problem given the compound observations. The filtering estimate is presented in the form of a continuous-discrete stochastic system with the martingales on the right-hand side. The article contains a description of a numerical algorithm implementing both process modeling in the considered observation system and the proposed solution for the filtering problem.