Higher Moments of Banach Space Valued Random Variables

ISBN-13: 9781470414658 / Angielski

Svante Janson;Sten Kaijser

Opis

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.

Spis treści

• Introduction
• Preliminaries
• Moments of Banach space valued random variables
• The approximation property Hilbert spaces $L^p(\mu)$ $C(K)$ $c_0(S)$ $D[0,1]$
• Uniqueness and convergence
• Appendix A. The reproducing Hilbert space
• Appendix B. The Zolotarev distances
• Bibliography