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Statistics of Random Processes pp 55–97Cite as

Conditionally Gaussian Sequences: Filtering and Related Problems

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Part of the book series: Stochastic Modelling and Applied Probability ((SMAP,volume 6))

Abstract

The two previous chapters dealt with problems of filtering, interpolation and extrapolation for the conditionally Gaussian processes (θ, ξ) in continuous time t ≥ 0. In the present chapter these problems will be investigated for random sequences with discrete time t = 0, ∆, 2∆, ..., having the property of ‘conditional normality’ as well.

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Notes and References

  1. Marsaglia, G. (1964): Conditional means and covariance of normal variables with singular covariance matrix. J. Am. Stat. Assoc., 308, 59, 1203–4

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  3. Gantmacher, F.R. (1967): Theory of Matrices. Nauka, Moscow

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  4. Liptser, R.S. and Shiryaev, A.N. (1972). Statistics of conditionally Gaussian random sequences. In: Proc. Sixth Berkeley Symposium on Mathematics, Statistics and Probability (1970), vol II. University of California Press, 389–422

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  5. Glonti, O.A. (1969): Sequential filtering and interpolation of Markov chain components. Litov. Mat. Sb., 9, 2, 263–79

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  6. Glonti, O.A. (1969): Extrapolation of Markov chain components. Litov. Mat. Sb., 9, 4, 741–54

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  7. Glonti, O.A. (1970): Sequential filtering of Markov chain components with singular diffusion matrices. Teor. Veroyatn. Primen., 15, 4, 736–40

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  8. Albert, A. (1972): Regression and the Moore-Penrose Pseudoinverse. Academic, New York London

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering Systems, Tel Aviv University, Ramat Aviv, P.O. Box 39040, 69978, Tel Aviv, Israel

    Robert S. Liptser

  2. Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 117966, Moscow, Russia

    Albert N. Shiryaev

Authors
  1. Robert S. Liptser
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  2. Albert N. Shiryaev
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© 2001 Springer-Verlag Berlin Heidelberg

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Liptser, R.S., Shiryaev, A.N. (2001). Conditionally Gaussian Sequences: Filtering and Related Problems. In: Statistics of Random Processes. Stochastic Modelling and Applied Probability, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10028-8_3

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  • DOI: https://doi.org/10.1007/978-3-662-10028-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08365-5

  • Online ISBN: 978-3-662-10028-8

  • eBook Packages: Springer Book Archive

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