Linear estimation of random processes

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


In the previous chapter the interrelation between properties in the “wide” and in the “narrow” sense frequently applied in probability theory was used in finding optimal linear estimates for stationary sequences with rational spectra. Thus it was enough for our purposes to consider the case of Gaussian sequences (Lemma 14.1) for the construction of the optimal mean square linear estimate. This technique will now be used in the problems of linear estimation of processes with continuous time. Here the consideration of the concept of a wide-sense Wiener process turns out to be useful.


Random Process Linear Estimate Wiener Process Nonlinear Estimate Fubini Theorem 
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Notes and references

  1. [147]
    Stratonovich R. L., Conditional Markov processes and their applications to the optimal control theory. Izd-vo MGU, 1966.Google Scholar
  2. [107]
    Liptser R. S., The comparison of nonlinear and linear filtering of Markov processes. Teoria Verojatn. i Primenen. XI, 3 (1966), 528–533.Google 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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