Skip to main content

On a formula relating the Shannon information to the fisher information for the filtering problem

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 61))

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.S. Liptser and A.N. Shiryayev: Statistics of Random Processes, Vols. I and II, Springer-Verlag, New York (1977).

    Google Scholar 

  2. M. Zakai: "On the optimal filtering of diffusion processes", Z. Wahr. Verw. Geb., 11 (1969), pp. 230–243.

    Google Scholar 

  3. M. Pinsker: Information and Information Stability of Random Variables and Processes, translated (from Russian) and edited by A. Feinstein, San Francisco, Holden Day (1964).

    Google Scholar 

  4. T.T. Kadota, M. Zakai and J. Ziv: "Mutual information of the white Gaussian channel with and without feedback", IEEE Trans. Infor. Theory, Vol. IT-17, 4 (1971), pp. 368–371.

    Google Scholar 

  5. H.L. Van Trees: Detection, Estimation and Modulation Theory, Part 1, New York, Wiley (1968).

    Google Scholar 

  6. B.Z. Bobrovski and M. Zakai: "A lower bound on the estimation of certain diffusion processes", IEEE Trans. Infor. Theory, Vol. IT-22, 1 (1976), pp. 45–52.

    Google Scholar 

  7. R.S. Liptser: "Optimal coding and decoding for transmission of a Gaussian Markov signal in a noiseless feedback channel", Probl. Peredachi Inform., 10, No. 4 (1974), pp. 3–15.

    Google Scholar 

  8. R.S. Bucy: "Information and Filtering", Information Sciences, 18 (1979), pp. 179–187.

    Google Scholar 

  9. B.Z. Bobrovski and M. Zakai: "Asymptotic a-priori estimates for the error in the nonlinear filtering problem", IEEE Trans. Infor. Theory, Vol. IT-28, 2 (1982), pp. 371–376.

    Google Scholar 

  10. B.L. Rozovskii, "On the Ito-Wentzel formula", Vestnik Moskov. Univ., No. 1 (1973), pp. 26–32.

    Google Scholar 

  11. H. Kunita: "Some extensions of Ito's formula", Séminaire de Probabilités XV, Lect. Notes in Math., 850, Springer-Verlag, Berlin-Heidelberg-New York, (1982), pp. 118–141.

    Google Scholar 

  12. J.M. Bismut: "A generalized formula of Ito and some other properties of stochastic flows", Z. Wahr. Verw. Geb., 55 (1981), pp. 331–350.

    Google Scholar 

  13. M.H.A. Davis and S.I. Marcus: "An introduction to nonlinear filtering", in Stochastic Systems: The Mathematics of Filtering and Identification, M. Hazewinkel and J.C. Willems (eds.), D. Reidel, Dortrecht (1981).

    Google Scholar 

  14. G. Kallianpur: Stochastic Filtering Theory, Springer-Verlag, New-York-Heidelberg-Berlin (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hayri Korezlioglu Gérald Mazziotto Jacques Szpirglas

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Mayer-Wolf, E., Zakai, M. (1984). On a formula relating the Shannon information to the fisher information for the filtering problem. In: Korezlioglu, H., Mazziotto, G., Szpirglas, J. (eds) Filtering and Control of Random Processes. Lecture Notes in Control and Information Sciences, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006569

Download citation

  • DOI: https://doi.org/10.1007/BFb0006569

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13270-7

  • Online ISBN: 978-3-540-38832-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics