An information theoretic view of stochastic resonance

We are motivated by the widely studied phenomenon called stochastic resonance, namely that in several sensing systems, both natural and engineered, the introduction of noise can enhance the ability of the system to perceive signals in the environment. We adopt an information theoretic viewpoint, evaluating the quality of sensing via the mutual information rate between the environmental signal and the observations. Viewing what would be considered noise in stochastic resonance as an open loop control and using Markov decision theory techniques, we discuss the problem of optimal choice of this control in order to maximize this mutual information rate. We determine the corresponding dynamic programming recursion: it involves the conditional law of certain conditional laws associated to the dynamics. We prove that the optimal control may be chosen as a deterministic function of this law of laws.