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Banach-space valued stationary processes with absolutely continuous spectral function

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Book cover Probability Theory on Vector Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 656))

Abstract

A generalization of a result of Miamee and Salehi on the factorization of positive operator valued functions on a Banach space is given. Also, two decomposition theorems for Banach-space valued stationary processes are proved, and the connections between the existence of moving averages representations and the regularity of a process on the one side and the absolutely continuity of his spectral function and the factorability of the corresponding density on the other side are investigated. Besides, some regularity conditions are discussed.

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References

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Authors and Affiliations

  1. Sektion Mathematik, Technische Universität, DDR - 8027, Dresden

    F. Schmidt

Authors
  1. F. Schmidt
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A. Weron

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© 1978 Springer-Verlag

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Schmidt, F. (1978). Banach-space valued stationary processes with absolutely continuous spectral function. In: Weron, A. (eds) Probability Theory on Vector Spaces. Lecture Notes in Mathematics, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068822

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  • DOI: https://doi.org/10.1007/BFb0068822

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08846-2

  • Online ISBN: 978-3-540-35814-5

  • eBook Packages: Springer Book Archive

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