The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 17, Number 3 (2007), 1102-1116.
Some relations between mutual information and estimation error in Wiener space
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.
Ann. Appl. Probab., Volume 17, Number 3 (2007), 1102-1116.
First available in Project Euclid: 22 May 2007
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 94A17: Measures of information, entropy
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60H35: Computational methods for stochastic equations [See also 65C30]
Mayer-Wolf, Eddy; Zakai, Moshe. Some relations between mutual information and estimation error in Wiener space. Ann. Appl. Probab. 17 (2007), no. 3, 1102--1116. doi:10.1214/105051607000000131. https://projecteuclid.org/euclid.aoap/1179839183