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Statistics of Random Processes II pp 50–89Cite as

Conditionally Gaussian sequences: filtering and related problems

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Part of the book series: Applications of Mathematics ((SMAP,volume 6))

Abstract

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.

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Notes and references

  1. Marsaglia G., Conditional means and covariance of normal variables with singular covariance matrix. J. Amer. Statist. Assoc. 59, 308 (1964), 1203–1204.

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  2. Anderson T., Introduction to the Multivariate Statistical Analysis. Russian transl., Fizmatgiz, Moscow, 1963.

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  3. Gantmacher F. R., The Theory of Matrices. “Nauka,” Moscow, 1967.

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  4. 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.

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  5. Glonti O. A., Sequential filtering and interpolation of Markov chain components. Litovsky matem sbornik IX, 2 (1969), 263–279 (Russian).

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  6. Glonti O. A., Extrapolation of Markov chain components. Litovsky matem. sbornik IX, 4 (1969), 741–754 (Russian).

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  7. Glonti O. A., Sequential filtering of Markov chain components with singular diffusion matrices. Teor. Verojatn. i Primenen, XV, 4 (1970), 736–740.

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Authors and Affiliations

  1. Institute for Problems of Control Theory, Profsojuznaja 81, Moscow, USSR

    R. S. Liptser

  2. Institute of Control Sciences, 117806, Moscow, USSR

    A. N. Shiryayev

Authors
  1. R. S. Liptser
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  2. A. N. Shiryayev
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© 1978 Springer Science+Business Media New York

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Liptser, R.S., Shiryayev, A.N. (1978). Conditionally Gaussian sequences: filtering and related problems. In: Statistics of Random Processes II. Applications of Mathematics, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4293-0_3

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  • DOI: https://doi.org/10.1007/978-1-4757-4293-0_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-4295-4

  • Online ISBN: 978-1-4757-4293-0

  • eBook Packages: Springer Book Archive

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