Cramér-Hida Representations from “First Principles”

Antonio F. Gualtierotti
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Antonio F. Gualtierotti: University of Lausanne, HEC and IDHEAP

Chapter Chapter 6 in Detection of Random Signals in Dependent Gaussian Noise, 2015, pp 433-504 from Springer

Abstract: 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].

Keywords: Orthogonal Increments; Management Part; Hahn-Hellinger Theorem; Absolute Continuity; Hilbert Space Valued (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22315-5_6

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