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COMPARISON OF WEAK AND STRONG MOMENTS FOR VECTORS WITH INDEPENDENT COORDINATES
Published online by Cambridge University Press: 14 February 2018
Abstract
We show that for $p\geqslant 1$, the
$p$th moment of suprema of linear combinations of independent centered random variables are comparable with the sum of the first moment and the weak
$p$th moment provided that
$2q$th and
$q$th integral moments of these variables are comparable for all
$q\geqslant 2$. The latest condition turns out to be necessary in the independent and identically distributed case.
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- Research Article
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- Copyright © University College London 2018
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