Titlebook: Detection of Random Signals in Dependent Gaussian Noise; Antonio F. Gualtierotti Book 2015 Springer International Publishing Switzerland 2

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https://doi.org/10.1007/978-981-19-0695-4Multiplicity is not easy to fathom. One way to acquire a feel for it, is to look at examples, and, in this chapter, multiplicity is looked at from different angles.

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https://doi.org/10.1007/978-981-19-0695-4One shall find below the stochastic calculus results required to state, and prove, a Girsanov’s formula tailored to the Cramér-Hida representation.

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https://doi.org/10.1007/978-3-86226-902-0The paths of ., a Cramér-Hida process, belong, almost surely, to the set

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Livestock and Women’s LivelihoodsThe model . (the SP.N model of the title) used so far has several potential limitations, summarized as the following items: a priori

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Reproducing Kernel Hilbert Spaces: The RudimentsThis chapter provides and illustrates, following the table of contents, the basic tools of the theory of reproducing kernel Hilbert spaces.

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Reproducing Kernel Hilbert Spaces and Paths of Stochastic ProcessesThe problem addressed in this chapter is that of giving conditions which insure that the paths of a stochastic process belong to a given RKHS, a requirement for likelihood detection problems not to be singular.

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Reproducing Kernel Hilbert Spaces and DiscriminationIn this chapter, it is examined to what extent RKHS’s allow one to discriminate between probability laws, that is determine their equivalence or singularity.

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Cramér-Hida Representations via Direct IntegralsDirect integrals generalize direct sums. As the CHR is a direct sum decomposition (preserving the time structure), it is perhaps unsurprising that direct integrals have a part to play in the study of the CHR.

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Some Facts About MultiplicityMultiplicity is not easy to fathom. One way to acquire a feel for it, is to look at examples, and, in this chapter, multiplicity is looked at from different angles.