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State Space Models for Gaussian Stochastic Processes

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Stochastic Systems: The Mathematics of Filtering and Identification and Applications

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 78))

Abstract

A comprehensive theory of stochastic realization for multivariate stationary Gaussian processes is presented. It is coordinate-free in nature, starting out with an abstract state space theory in Hilbert space, based on the concept of splitting subspace. These results are then carried over to the spectral domain and described in terms of Hardy functions. Each state space is uniquely characterized by its structural function, an inner function which contains all the systems theoretical characteristics of the corresponding realizations. Finally coordinates are introduced and concrete differential-equation-type representations are obtained. This paper is an abridged version of a forthcoming paper, which in turn summarizes and considerably extends results which have previously been presented in a series of preliminary conference papers.

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Author information

Authors and Affiliations

  1. University of Kentucky, Lexington, Kentucky, USA

    Anders Lindquist & Giorgio Picci

  2. LADSEB-CNR, Padova, Italy

    Anders Lindquist & Giorgio Picci

Authors
  1. Anders Lindquist
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  2. Giorgio Picci
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Editor information

Editors and Affiliations

  1. Erasmus Universiteit, Rotterdam, The Netherlands

    Michiel Hazewinkel

  2. Rijksuniversiteit, Groningen, The Netherlands

    Jan C. Willems

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© 1981 D. Reidel Publishing Company

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Lindquist, A., Picci, G. (1981). State Space Models for Gaussian Stochastic Processes. In: Hazewinkel, M., Willems, J.C. (eds) Stochastic Systems: The Mathematics of Filtering and Identification and Applications. NATO Advanced Study Institutes Series, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8546-9_10

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  • DOI: https://doi.org/10.1007/978-94-009-8546-9_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8548-3

  • Online ISBN: 978-94-009-8546-9

  • eBook Packages: Springer Book Archive

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