TY - JOUR
T1 - Decoupling of Banach-valued multilinear forms in independent symmetric Banach-valued random variables
AU - McConnell, Terry R.
AU - Taqqu, Murad S.
PY - 1987/8
Y1 - 1987/8
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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U2 - 10.1007/BF00320330
DO - 10.1007/BF00320330
M3 - Article
AN - SCOPUS:34250099606
SN - 0178-8051
VL - 75
SP - 499
EP - 507
JO - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
JF - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
IS - 4
ER -