Higher moments of Banach space valued random variables

We define the 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 va...

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Bibliographische Detailangaben
Hauptverfasser: Janson, Svante, Kaijser, Sten
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2015
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Banach spaces
Random variables
approximation property
projective tensor product
<inline-formula content-type="math/mathml"> D [ 0 , 1 ] D[0, 1] </inline-formula>
Banach space valued random variable
injective tensor product
Bochner integral
Dunford integral
Zolotarev metrics
Pettis integral
ISBN:1470414651, 9781470414658
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:We define the 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, 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.
Bibliographie:Bibliography: p. 107-110
ISBN:1470414651
9781470414658
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1127