Geodesic
Interpolation and filtering of a~jump-like component of a~Markov process
Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 853-865.

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Stochastic differential equations are introduced for a posteriori probabilities in problems of estimating a Markov process with a denumerable set of states on the basis of a process which admits the stochastic differential (1). 
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R. Sh. Liptser; A. N. Shiryaev. Interpolation and filtering of a~jump-like component of a~Markov process. Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 853-865. http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a7/

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