Conditionally Gaussian sequences: filtering and related problems

  • R. S. Liptser
  • A. N. Shiryayev
Part of the Applications of Mathematics book series (SMAP, volume 6)


The two previous chapters dealt with problems of filtering, interpolation and extrapolation for the conditionally Gaussian random processes (θ ξ), in continuous time t ≥ O. In the present chapter these problems will be investigated for random sequences with discrete time t = 0, Δ, 2Δ,. . ., having the property of “conditional Gaussianness” as well.


Conditional Distribution Normal Correlation Recursive Equation Gaussian Vector Gaussian Sequence 
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Notes and references

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    Marsaglia G., Conditional means and covariance of normal variables with singular covariance matrix. J. Amer. Statist. Assoc. 59, 308 (1964), 1203–1204.zbMATHCrossRefGoogle Scholar
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    Anderson T., Introduction to the Multivariate Statistical Analysis. Russian transl., Fizmatgiz, Moscow, 1963.Google Scholar
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    Gantmacher F. R., The Theory of Matrices. “Nauka,” Moscow, 1967.Google Scholar
  4. [119]
    Liptser R. S., Shiryayev A. N., Statitistics of Conditionally Gaussian Random Sequences. Proc. Sixth Berkeley Sympos. Math. Statistics and Probability (1970), Vol. II, Univ. of Calif. Press, 1972, 389–422.Google Scholar
  5. [38]
    Glonti O. A., Sequential filtering and interpolation of Markov chain components. Litovsky matem sbornik IX, 2 (1969), 263–279 (Russian).MathSciNetGoogle Scholar
  6. [39]
    Glonti O. A., Extrapolation of Markov chain components. Litovsky matem. sbornik IX, 4 (1969), 741–754 (Russian).MathSciNetGoogle Scholar
  7. [40]
    Glonti O. A., Sequential filtering of Markov chain components with singular diffusion matrices. Teor. Verojatn. i Primenen, XV, 4 (1970), 736–740.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • R. S. Liptser
    • 1
  • A. N. Shiryayev
    • 2
  1. 1.Institute for Problems of Control TheoryMoscowUSSR
  2. 2.Institute of Control SciencesMoscowUSSR

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