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arXiv · 1612.02407

Comparison of weak and strong moments for vectors with independent coordinates

Rafał Latała·Marta Strzelecka
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Abstract

We show that for $p\ge 1$, 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 \ge 2$. The latest condition turns out to be necessary in the i.i.d. case.

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Rafał Latała, Marta Strzelecka. 2016-12-07. Comparison of weak and strong moments for vectors with independent coordinates. https://doi.org/10.1112/s0025579317000432

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