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Some relations between mutual information and estimation error in Wiener space

Eddy Mayer-Wolf·Moshe Zakai
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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.

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Eddy Mayer-Wolf, Moshe Zakai. 2007-07-31. Some relations between mutual information and estimation error in Wiener space. https://doi.org/10.1214/105051607000000131

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