Question

Why is the covariance operator of a Gaussian measure not defined on the dual space?

score 44 · Answer 1 · 2024-03-20 20:25:34

44

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Why is the covariance operator of a Gaussian measure not defined on the dual space?

Published on 20 Mar 2024 - 20:25

score 335 · Answer 2 · 2021-03-12 07:13:34

335

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Reference: Covariance operator is compact

Published on 12 Mar 2021 - 7:13

score 107 · Answer 3 · 2026-02-23 11:49:07

107

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Construction and properties of an Abstract Wiener Process on $C(\mathbb{R}^n,\mathbb{R}^n)$

Published on 23 Feb 2026 - 11:49

score 256 · Answer 4 · 2021-04-28 10:30:03

256

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Abstract Wiener Space for $\ell^2(\mathbb{R})$

Published on 28 Apr 2021 - 10:30

score 177 · Answer 5 · 2021-04-29 15:08:48

177

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Holder-continuity of the fractional Brownian motion in a compact $[0,T]$ and dependence in $T$

Published on 29 Apr 2021 - 15:08

score 94 · Answer 6 · 2021-06-18 09:23:13

94

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How does the Cameron-Martin space of a Gaussian Markov process with initial condition $0$ change when we consider a random initial condition

Published on 18 Jun 2021 - 9:23

score 491 · Answer 7 · 2021-06-24 16:58:09

491

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Cameron-Martin space has measure $1$ and also $0$?

Published on 24 Jun 2021 - 16:58

score 113 · Answer 8 · 2021-09-22 10:24:49

113

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Show that the covariance operator of a Gaussian measure is uniquely determined and nonnegative

Published on 22 Sep 2021 - 10:24

score 24 · Answer 9 · 2021-10-15 02:54:29

24

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Reference request: sequence of Gaussians in $\ell^2(\mathbb{N})$

Published on 15 Oct 2021 - 2:54

score 107 · Answer 10 · 2021-11-02 14:13:31

107

Views

Gaussian Expectation, using maximum

Published on 02 Nov 2021 - 14:13

score 138 · Answer 11 · 2021-11-11 16:53:51

138

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If a Gaussian measure has density, then its covariance is nondegenerate

Published on 11 Nov 2021 - 16:53

score 200 · Answer 12 · 2021-11-27 22:02:49

200

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Energy Distance between Multivariate Gaussian Distributions

Published on 27 Nov 2021 - 22:02

score 42 · Answer 13 · 2022-01-10 12:56:55

42

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$1-e^{-\frac{1}{2} \langle Qh, h\rangle_U} = \int_U (1-\cos \langle h , x\rangle_U )\mu(dx)$ where $Q$ is the covariance operator of Gaussian $\mu$

Published on 10 Jan 2022 - 12:56

score 107 · Answer 14 · 2022-01-27 02:17:40

107

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Unit ball of a Banach space with zero-mean Gaussian measure

Published on 27 Jan 2022 - 2:17

score 47 · Answer 15 · 2022-03-28 20:25:33

47

Views

Geometry of Voronoi cells of $n+1$ equidistant points in $\mathbb{R}^n$

Published on 28 Mar 2022 - 20:25

List Question

Why is the covariance operator of a Gaussian measure not defined on the dual space?

Reference: Covariance operator is compact

Construction and properties of an Abstract Wiener Process on $C(\mathbb{R}^n,\mathbb{R}^n)$

Abstract Wiener Space for $\ell^2(\mathbb{R})$

Holder-continuity of the fractional Brownian motion in a compact $[0,T]$ and dependence in $T$

How does the Cameron-Martin space of a Gaussian Markov process with initial condition $0$ change when we consider a random initial condition

Cameron-Martin space has measure $1$ and also $0$?

Show that the covariance operator of a Gaussian measure is uniquely determined and nonnegative

Reference request: sequence of Gaussians in $\ell^2(\mathbb{N})$

Gaussian Expectation, using maximum

If a Gaussian measure has density, then its covariance is nondegenerate

Energy Distance between Multivariate Gaussian Distributions

$1-e^{-\frac{1}{2} \langle Qh, h\rangle_U} = \int_U (1-\cos \langle h , x\rangle_U )\mu(dx)$ where $Q$ is the covariance operator of Gaussian $\mu$

Unit ball of a Banach space with zero-mean Gaussian measure

Geometry of Voronoi cells of $n+1$ equidistant points in $\mathbb{R}^n$

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