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COMPARISON OF WEAK AND STRONG MOMENTS FOR VECTORS WITH INDEPENDENT COORDINATES

  • Rafał Latała (a1) and Marta Strzelecka (a2)

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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