Scope of Signal Plus “White Noise” Model (III)

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

Chapter Chapter 16 in Detection of Random Signals in Dependent Gaussian Noise, 2015, pp 993-1085 from Springer

Abstract: Abstract Cramér-Hida processes have components that are continuous, Gaussian martingales. One may wonder what happens when one drops the Gaussian assumption, since, as seen, continuous martingales are time changed Wiener processes [264, p. 213]. One shall see that Girsanov’s theorem loses then its strength to the point that the family of signals admissible for the computation of likelihoods becomes practically useless (signals must depend on the quadratic variation of the noise). But the road to establishing that fact is long and tortuous, though quite interesting. It also often requires the assumption that probability spaces are complete. The standard assumption for the section shall thus be that basic probability spaces are complete, and that σ-algebras contained in the “mother” σ-algebras contain the sets of measure zero of the latter.

Keywords: Girsanov; Basic Probability Space; Quadratic Variation; Gaussian Martingale; Local Martingale (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22315-5_16

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