Some relations between mutual information and estimation error in Wiener space
Probability
2009-09-29 v2
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.
Cite
@article{arxiv.math/0610024,
title = {Some relations between mutual information and estimation error in Wiener space},
author = {Eddy Mayer-Wolf and Moshe Zakai},
journal= {arXiv preprint arXiv:math/0610024},
year = {2009}
}
Comments
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)