Higher Moments of Banach Space Valued Random Variables is popular PDF and ePub book, written by Svante Janson in 2015, it is a fantastic choice for those who relish reading online the Banach spaces genre. Let's immerse ourselves in this engaging Banach spaces book by exploring the summary and details provided below. Remember, Higher Moments of Banach Space Valued Random Variables can be Read Online from any device for your convenience.
Higher Moments of Banach Space Valued Random Variables Book PDF Summary
We 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. We 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. One of the problems studied is whether two random variables with the same injective moments (of a given order) necessarily have the same projective moments; this is of interest in applications. We show that this holds if the Banach space has the approximation property, but not in general. Several chapters are devoted to results in special Banach spaces, including Hilbert spaces, C(K) and D[0, 1]. The latter space is non-separable, which complicates the arguments, and we prove various preliminary results on e.g. measurability in D[0, 1] that we need. One of the main motivations of this paper is the application to Zolotarev metrics and their use in the contraction method. This is sketched in an appendix.
Detail Book of Higher Moments of Banach Space Valued Random Variables PDF
- Author : Svante Janson
- Release : 01 October 2024
- Publisher : Unknown
- ISBN : 147042617X
- Genre : Banach spaces
- Total Page : 110 pages
- Language : English
- PDF File Size : 20,6 Mb
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