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Cramér-Hida Representations from “First Principles”

In: Detection of Random Signals in Dependent Gaussian Noise

Author

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  • Antonio F. Gualtierotti

    (University of Lausanne, HEC and IDHEAP)

Abstract

The Cramér-Hida representation shall be, at first, the decomposition of a function, with values in a Hilbert space, into manageable parts, one continuous, and one discontinuous. The continuous part shall furthermore be decomposed into a possibly infinite sum of continuous and orthogonal functions, which have a representation as integrals, with respect to an orthogonal vector measure, itself determined by a function with orthogonal increments. The decomposition is obtained under some “natural” assumptions [Assumption 6.4.1].

Suggested Citation

  • Antonio F. Gualtierotti, 2015. "Cramér-Hida Representations from “First Principles”," Springer Books, in: Detection of Random Signals in Dependent Gaussian Noise, chapter 0, pages 433-504, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22315-5_6
    DOI: 10.1007/978-3-319-22315-5_6
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