On Equations for Shannon Information in Transmission of Markov Diffusion Signals Through Channels with Memory

We derive equations for Shannon information in transmission of a multidimensional Markov diffusion signal through a multidimensional channel, when the output signal carries information not only about the current value of the transmitted signal but also about its past value with some fixed delay. We consider both continuous and continuous-discrete transmission, when the receiver input is a collection of realizations of continuous and discrete stochastic processes.