Some relations between mutual information and estimation error in Wiener space

Abstract

The model considered is that of “signal plus white noise.” Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The results are shown to be invariant under a wide class of causality patterns; they are applied to the derivation of the causal estimation error of a Gaussian nonstationary filtering problem and to a multidimensional extension of the Yovits–Jackson formula.