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  1. 54 On Sub-Gaussianity in Banach Spaces A random element ξ: Ω →X is called Gaussian, if for each functional x∗∈X∗, the random variable x∗,ξ is Gaussian. A mapping R: X∗→Xis said to be a Gaussian covariance if there exists a Gaussian random element in X, the covariance operator of which is R.
  2. publishing.ug.edu.ge

    Banach space [2]. For ξ ∈SG(Ω) instead of τ(ξ) we will write also ξ SG(Ω). More information about the sub-Gaussian random variables can be found for example in [5], [6]. Let X be a Banach space over R with a norm · and X∗ be its dual space. The value of the linear functional x∗ ∈X∗ at an element x∈X is denoted by the symbol x ...
  3. math.stackexchange.com

    Nov 28, 2024Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
  4. dept.math.lsa.umich.edu

    An Introduction to Banach Space Theory Robert E. Megginson Graduate Texts in Mathematics 183 Springer-Verlag New York, Inc. October, 1998. Acknowledgment: I wish to express my gratitude to Allen Bryant, who worked through the initial part of Chapter 2 while a graduate student at Eastern Illinois University and caught several errors that were corrected before this book saw the light of day.
  5. link.springer.com

    Feb 16, 2023As is evident from the proof of the second part of Theorem 3.3.2, there are many choices of the Banach space for a given Hilbert space even though there is only one Hilbert space for a given Banach space. Thus, when thinking in terms of abstract Wiener spaces, the canonical object is the Hilbert space.
  6. link.springer.com

    72 3 Gaussian Measures on a Banach Space Lemma 3.2.2 If B is a separable Banach space, then B B is the smallest σ-algebra withrespecttowhichx ∈ B x,ξ∈ Rismeasurableforallξ ∈ B∗.Inparticular, if μ, ν ∈ M 1(E), then μ = ν if and only if μˆ =ˆν. Proof Clearly x ∈ B −→ x,ξ∈ RisB B measurableforallξ ∈ B∗.Toprovethat sets in B B are measurable with respect to the ...
  7. sas.rochester.edu

    Definition 2.2.X is a Banach space if X is a vector space with kk: X ! R+ satisfying kvk = 0 iffv = 0, kavk = jajkvk, ku+vk kuk+kvk, (8)a 2 F, u,v 2 X, and (X,d) is a complete metric space with d(u,v) := ku vk, (8)u,v 2 X. An important category of Banach spaces are the Hilbert spaces. Definition 2.3.X is a Hilbert space if X is a Banach space ...
  8. cambridge.org

    Thus, in this chapter, we will look at Wiener measure from a strictly Gaussian point of view. More generally, we will be dealing here with measures on a real Banach space E that are centered Gaussian in the sense that, for each x * in the dual space E *, x ∈ E ↦ 〈 x, x *〉, ∈ ℝ is a centered Gaussian
  9. files.ele-math.com

    spaces have been used in analysis, for example, see [3, 13]. Motivated by mentioned references, we will discuss Banach space valued Bochner-Lebesgue spaces with vari-able exponent. In what follows, (A,A ,μ) will be a σ-finite complete measure space. Suppose D is a subsetof A, let χ D be the indicatorfunctionon D. Let E be a Banach space ...
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