Abstract
This chapter deals with some of the properties of Gaussian measures and the construction of families of Gaussian random variables.
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Notes
- 1.
Even though some of the vectors involved are complex, the inner product here is the Euclidean one, not the Hermitian one.
- 2.
\(\Vert A\Vert _{\textrm{op}}\) is the operator norm \(\sup \{|Ax|:\,|x|=1\}\) of A, which, because A is symmetric and positive definite, equals \(\sup \{(x,Ax)_{{\mathbb R}^N}:\,|x|=1\}\).
- 3.
Its sufficiency was proved by Dudley, and its necessity was proved later by Talagrand.
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Stroock, D.W. (2023). Gaussian Measures and Families. In: Gaussian Measures in Finite and Infinite Dimensions. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-031-23122-3_2
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DOI: https://doi.org/10.1007/978-3-031-23122-3_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-23121-6
Online ISBN: 978-3-031-23122-3
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