2007/10/05 by Piera, Francisco J., Parada, Patricio
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.0710.1280
We consider a general stochastic input-output dynamical system with output evolving in time as the solution to a functional coefficients, Itô's stochastic differential equation, excited by an input process. This general class of stochastic systems encompasses not only the classical communication channel models, but also a wide variety of engineering systems appearing through a whole range of applications. For this general setting we find analogous of known relationships linking input-output mutual information and minimum mean causal and non-causal square errors, previously established in the context of additive Gaussian noise communication channels. Relationships are not only established in terms of time-averaged quantities, but also their time-instantaneous, dynamical counterparts are presented. The problem of appropriately introducing in this general framework a 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.