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Higher Moments of Banach Space Valued Random Variables.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2015Copyright date: ©2015Edition: 1st edDescription: 1 online resource (124 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470426170
Subject(s): Genre/Form: Additional physical formats: Print version:: Higher Moments of Banach Space Valued Random VariablesDDC classification:
  • 515/.732
LOC classification:
  • QA273.J367 2015
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Notations -- 2.2. Measurability -- 2.3. Tensor products of Banach spaces -- 2.4. Vector-valued integration -- Chapter 3. Moments of Banach space valued random variables -- 3.1. Moments -- 3.2. Examples -- Chapter 4. The approximation property -- Chapter 5. Hilbert spaces -- Chapter 6. ^{ }( ) -- Chapter 7. ( ) -- Chapter 8. ₀( ) -- Chapter 9. [0,1] -- 9.1. [0,1] as a Banach space -- 9.2. [0,1] as a Banach algebra -- 9.3. Measurability and random variables in \doi -- 9.4. Moments of [0,1]-valued random variables -- Chapter 10. Uniqueness and Convergence -- 10.1. Uniqueness -- 10.2. Convergence -- Appendix A. The Reproducing Hilbert Space -- Appendix B. The Zolotarev Distances -- B.1. Fréchet differentiablity -- B.2. Zolotarev distances -- Bibliography -- Back Cover.
Summary: The authors define the k:th moment of a Banach space valued random variable as the expectation of its k:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
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Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Notations -- 2.2. Measurability -- 2.3. Tensor products of Banach spaces -- 2.4. Vector-valued integration -- Chapter 3. Moments of Banach space valued random variables -- 3.1. Moments -- 3.2. Examples -- Chapter 4. The approximation property -- Chapter 5. Hilbert spaces -- Chapter 6. ^{ }( ) -- Chapter 7. ( ) -- Chapter 8. ₀( ) -- Chapter 9. [0,1] -- 9.1. [0,1] as a Banach space -- 9.2. [0,1] as a Banach algebra -- 9.3. Measurability and random variables in \doi -- 9.4. Moments of [0,1]-valued random variables -- Chapter 10. Uniqueness and Convergence -- 10.1. Uniqueness -- 10.2. Convergence -- Appendix A. The Reproducing Hilbert Space -- Appendix B. The Zolotarev Distances -- B.1. Fréchet differentiablity -- B.2. Zolotarev distances -- Bibliography -- Back Cover.

The authors define the k:th moment of a Banach space valued random variable as the expectation of its k:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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