Summary
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 (j)i } and {r (j)i } for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities
and their “decoupled” versions
, for Bochner integrable F i : [0, 1]d→E. This generalizes results of Kwapień and of Zinn.
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Supported in part by NSF grant DMS 85-03775 and by the Sloan Foundation
Supported in part by NSF grant ECS 84-08524
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McConnell, T.R., Taqqu, M.S. Decoupling of Banach-valued multilinear forms in independent symmetric Banach-valued random variables. Probab. Th. Rel. Fields 75, 499–507 (1987). https://doi.org/10.1007/BF00320330
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DOI: https://doi.org/10.1007/BF00320330