Decoupling of Banach-valued multilinear forms in independent symmetric Banach-valued random variables

Autor: Murad S. Taqqu, Terry R. McConnell
Rok vydání: 1987
Předmět:
Zdroj: Probability Theory and Related Fields. 75:499-507
ISSN: 1432-2064
0178-8051
DOI: 10.1007/bf00320330
Popis: Let E be a Banach space and Π: E→ℝ+ be symmetric, continuous and convex. Let {Ui} and {ri} be independent sequences of random variables having, respectively, U(0, 1) and symmetric Bernoulli distributions, and let {U i (j) } and {r i (j) } for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities $$E\Phi (\sum\limits_{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{i} \in \mathbb{Z}_ + ^d } {r_{i_1 } } ...r_{i_d } F_{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{i} } (U_{i_1 } ,...,U_{i_d } ))$$ and their “decoupled” versions $$E\Phi (\sum\limits_{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\iota } \in \mathbb{Z}_ + ^d } {r_{i_1 }^{(1)} ...r_{i_d }^{(d)} } F_{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\iota } } (U_{i_1 }^{(1)} ,..., U_{i_d }^{(d)} ))$$ , for Bochner integrable F i : [0, 1] d →E. This generalizes results of Kwapien and of Zinn.
Databáze: OpenAIRE
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