A Theorem by Liptser and Shiryayev

  • Peter A. Ruymgaart
  • Tsu T. Soong
Part of the Springer Series in Information Sciences book series (SSINF, volume 14)


A relatively complete mathematical development of the Kalman-Bucy filter has been presented in Chap. 4. One of the results that emerged in this discourse is the fact that success of the filter depends on the contamination of observation by white noise, much like dimming the light to see more clearly. The purpose of this short chapter is to shed some light on this self-contradictory phenomenon through a theorem by Liptser and Shiryayev.


White Noise Orthonormal Base Orthogonal Projection Spectral Representation Variance Estimator 
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  1. 5.1
    M. Loève: Probability Theory (Van Nostrand, Princeton 1955)MATHGoogle Scholar
  2. 5.2
    R. S. Liptser, A. N. Shiryayev: Statistics of Random Process I, General Theory, Applications of Mathematics, Vol. 5 (Springer, Berlin, Heidelberg, New York 1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Peter A. Ruymgaart
    • 1
  • Tsu T. Soong
    • 2
  1. 1.Department of MathematicsUniversity of Technology, DelftDelftThe Netherlands
  2. 2.Faculty of Engineering and Applied SciencesState University of New York at BuffaloBuffaloUSA

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