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

Terry R. McConnell; Murad S. Taqqu

doi:10.1007/BF00320330

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

Terry R. McConnell, Murad S. Taqqu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let E be a Banach space and Π: E→ℝ₊ be symmetric, continuous and convex. Let {U_i} and {r_i} 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 {Mathematical expression} and their "decoupled" versions {Mathematical expression}, for Bochner integrable F_i: [0, 1]^d→E. This generalizes results of Kwapień and of Zinn.

Original language	English (US)
Pages (from-to)	499-507
Number of pages	9
Journal	Probability Theory and Related Fields
Volume	75
Issue number	4
DOIs	https://doi.org/10.1007/BF00320330
State	Published - Aug 1987

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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abstract = "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 {Ui(j)} and {ri(j)} for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities {Mathematical expression} and their {"}decoupled{"} versions {Mathematical expression}, for Bochner integrable Fi: [0, 1]d→E. This generalizes results of Kwapie{\'n} and of Zinn.",

author = "McConnell, {Terry R.} and Taqqu, {Murad S.}",

year = "1987",

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AU - Taqqu, Murad S.

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N2 - 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 {Ui(j)} and {ri(j)} for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities {Mathematical expression} and their "decoupled" versions {Mathematical expression}, for Bochner integrable Fi: [0, 1]d→E. This generalizes results of Kwapień and of Zinn.

AB - 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 {Ui(j)} and {ri(j)} for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities {Mathematical expression} and their "decoupled" versions {Mathematical expression}, for Bochner integrable Fi: [0, 1]d→E. This generalizes results of Kwapień and of Zinn.

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ER -

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

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