Some relations between mutual information and estimation error in wiener space

Annals of Applied Probability

Volumn 17, Issue 3, 2007, Pages 1102-1116

  Mayer Wolf, Eddy ^a   Zakai, Moshe ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Abstract wiener space; Causality; Estimation errors; Mutual information; Resolution of identity

Indexed keywords

EID: 52349110462     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051607000000131     Document Type: Article

References (13)

1. DUNCAN, T. E. (1970). On the calculation of mutual information. SIAM J. Appl. Math. 19 215-220. MR0289205
2. GRENANDER, U. and SZEGÖ, G. (1958). Toeplitz Forms and Their Applications. Univ. California Press, Berkeley. MR0094840
3. GUO, D., SHAMAI, S. and VERDÚ, S. (2005). Mutual information and minimum mean-square error in estimation, filtering and smoothing. IEEE Trans. Inform. Theory 51 1261-1282. MR2241490
4. KAC, M., MURDOCK, W. L. and SZEGO, G. (1953). On the eigenvalues of certain Hermitian forms. Indiana Univ. Math. J. (formerly J. Rational Mech. Anal.) 2 767-800. MR0059482
5. KADOTA, T. T., ZAKAI, M. and ZIV, J. (1971). Mutual information of the white Gaussian channel with and without feedback. IEEE Trans. Inform. Theory IT-17 368-371. MR0406696
6. LERER, L. E. (1978). On approximating the spectrum of convolution-type operators. I. Wiener-Hopf matricial integral operators. Israel J. Math. 30 339-362. MR0506376
7. PINSKER, M. S. (1964). Information and Information Stability of Random Variables and Processes. Holden-Day, San Francisco, CA. MR0213190
8. SNYDERS, J. (1972). Error formulae for optimal linear filtering, prediction and interpolation of stationary time series. Ann. Math. Statist. 43 1935-1943. MR0353442
9. SNYDERS, J. (1972). Error expressions for optimal linear filtering of stationary processes. IEEE Trans. Inform. Theory IT-18 574-582. MR0453137
10. ÜSTÜNEL, A. S. and ZAKAI, M. (2000). Transformation of Measure on Wiener Space. Springer, Berlin. MR1736980
11. ÜSTÜNEL, A. S. and ZAKAI, M. (1997). The construction of filtrations on abstract Wiener space. Func. Anal. 143 10-32. MR1428114
12. YOVITS, M. C. and JACKSON, J. L. (1955). Linear filter optimization with game theory considerations. In IRE Nat. Conv. Rec. 4 193-199.
13. ZAKAI, M. (2005). On mutual information, likelihood ratios, and estimation error for the additive Gaussian channel. IEEE Trans. Inform. Theory 51 3017-3024. MR2239133