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Comparison of weak and strong moments for vectors with independent coordinates
Rafał Latała, Marta Strzelecka · 2016-12-08 · via math.PR updates on arXiv.org

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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