Sharp L1(ℓq) estimate for a sequence and its predictable projection

Adam Osȩkowski

Statistics & Probability Letters, 2015, vol. 104, issue C, 82-86

Abstract: Let f=(fn)n≥0 be a sequence of integrable Banach-space valued random variables and g=(gn)n≥0 denote its predictable projection. We prove that, for 1≤q<∞, E(∑n=0∞|gn|q)1/q≤2(q−1)/qE(∑n=0∞|fn|q)1/q and that the constant 2(q−1)/q is the best possible. The proof rests on the construction of a certain special function enjoying appropriate majorization and concavity.

Keywords: Predictable projection; Best constants (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.05.005

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