TY  - BOOK
AU  - Janson,Svante
AU  - Kaijser,Sten
TI  - Higher Moments of Banach Space Valued Random Variables
T2  - Memoirs of the American Mathematical Society
SN  - 9781470426170
AV  - QA273.J367 2015 
U1  - 515/.732 
PY  - 2015///
CY  - Providence
PB  - American Mathematical Society
KW  - Random variables
KW  - Electronic books
N1  - 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
N2  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832037
ER  -