Filtration of Time-Continuous Stochastic Signals by Discrete Observations With Memory

The problem of filtration of a multidimensional stochastic signal of the Markov diffusion type is considered under the condition that the observed time-discrete multidimensional random process depends not only on the current value of the useful signal, but also on an arbitrary number of its past values. For a particular case, the efficiency of a channel with memory of multiplicity two with respect to a channel without memory is investigated.