On the connections between information and estimation theory: from AWGN Channels to dynamical systems with feedback

We consider a stochastic dynamical system whose output evolves in time as the solution to a functional coefficients, Itopsilas stochastic differential equation, excited by an input process. This general class of stochastic systems encompasses a wide variety of engineering models appearing through a whole range of applications, extending in particular the classical communication channel models. We find analogous of known relationships linking input-output mutual information and causal and noncausal minimum mean-square errors in the context of additive Gaussian noise communication channels. The introduction in this general framework of an appropriate signal-to-noise ratio notion expressed through a signal-to-noise ratio parameter is also taken into account, identifying conditions for a proper and meaningful interpretation.