Higher Moments of Banach Space Valued Random Variables.
Janson, Svante.
Higher Moments of Banach Space Valued Random Variables. - 1st ed. - 1 online resource (124 pages) - Memoirs of the American Mathematical Society ; v.238 . - Memoirs of the American Mathematical Society .
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.
9781470426170
Random variables.
Electronic books.
QA273.J367 2015
515/.732
Higher Moments of Banach Space Valued Random Variables. - 1st ed. - 1 online resource (124 pages) - Memoirs of the American Mathematical Society ; v.238 . - Memoirs of the American Mathematical Society .
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.
9781470426170
Random variables.
Electronic books.
QA273.J367 2015
515/.732