uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Higher moments of Banach space valued random variables
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Memoirs of the American Mathematical Society, ISSN 0065-9266, E-ISSN 1947-6221, Vol. 238, no 1127, 1-110 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 238, no 1127, 1-110 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-287527DOI: 10.1090/memo/1127ISI: 000372829500001OAI: oai:DiVA.org:uu-287527DiVA: diva2:922888
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-04-25 Created: 2016-04-25 Last updated: 2016-05-25Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Janson, SvanteKaijser, Sten
By organisation
Analysis and Probability Theory
In the same journal
Memoirs of the American Mathematical Society
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 83 hits
ReferencesLink to record
Permanent link

Direct link