Mutual information for stochastic signals and fractional Brownian motion

IEEE Transactions on Information Theory

Volumn 54, Issue 10, 2008, Pages 4432-4438

  Duncan, Tyrone E ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

Additives; Calculus; Estimation; Estimation error; Fractional Brownian motion; Fractional Gaussian noise; Gaussian noise; Likelihood functions; Mutual information; Stochastic processes

Indexed keywords

EID: 54749145122     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.928995     Document Type: Article

References (15)

1. T. E. Duncan, "On the calculation of mutual information," SIAM J. Appl. Math., vol. 19, pp. 215-220, 1970.
2. D. Guo, S. Shamai, and S. Verdú, "Mutual information and minimum mean square error in Gaussian channels," IEEE Trans. Inf. Theory, vol. 51, pp. 1261-1282, 2005.
3. M. Zakai, "On mutual information, likelihood ratios and estimation error for the additive Gaussian channel," IEEE Trans. Inf. Theory vol. 51,pp.3017-3024, 2005.
4. E. Mayer-Wolf and M. Zakai, "For relations between mutual information and estimation error in Wiener space," Ann. Appl. Prob, vol. 17, pp.1102-1117, 2007.
5. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. New York: Gordon and Breach, 1993.
6. E. Alòs, O. Mazet, and D. Nualart, "Stochastic calculus with respect to Gaussian processes," Ann. Probab., vol. 29, no. 2, pp. 766-801, 2001.
7. T. E. Duncan, Y. Hu, and B. Pasik-Duncan, "Stochastic calculus for fractional Brownian motion I. Theory," SIAM J. Contr. Optim., vol. 38, no. 2, pp. 582-612, 2000.
8. T. E. Duncan, J. Jakubowski, and B. Pasik-Duncan, "Stochastic integration for fractional Brownian motion in a Hilbert space," Stoch. Dyn., vol. 6, pp. 53-75, 2006.
9. I. M. Gelfand and A. M. Yaylom, "Calculation of the amount of information about a random function in another such function," Uspekhi Mat. Nauk., vol. 12, pp. 3-52, 1957.
10. I. V. Girsanov, "On transforming a class of stochastic process by absolutely continuous substitution of measures," Teor. Verojatnost. i Primenen, vol. 5, pp. 314-330, 1960.
11. T. E. Duncan, B. Maslowski, and B. Pasik-Duncan, "Semilinear stochastic equations in a Hilbert space with a fractional Brownian motion," SIAM J. Math. Anal., to be published.
12. D. Feyel and A. d. I. Pradelle, "On fractional Brownian processes," Potential Anal., vol. 10, pp. 273-288, 1999.
13. T. E. Duncan, "Evaluation of likelihood function," Inf. Contr., vol. 13, pp.62-74, 1968.
14. D. Nualart, The Malliavin Calculus and Related Topics, Second ed. New York: Springer-Verlag, 2005.
15. Y. Hu and B. Oksendal, "Wick approximation of quasilinear stochastic differential equations," Stoch. Anal. Rel. Topics V, pp. 203-231, 1996.