Some relations between mutual information and estimation error in Wiener space
arXiv:math/0610024 · doi:10.1214/105051607000000131
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.
Published at http://dx.doi.org/10.1214/105051607000000131 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)