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COMPARISON OF WEAK AND STRONG MOMENTS FOR VECTORS WITH INDEPENDENT COORDINATES

Part of: Probability theory on algebraic and topological structures Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  14 February 2018

Rafał Latała  and
Marta Strzelecka
Rafał Latała
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02–097 Warsaw, Poland email rlatala@mimuw.edu.pl
Marta Strzelecka
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02–097 Warsaw, Poland email martast@mimuw.edu.pl
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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.

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 60G50: Sums of independent random variables; random walks
Secondary: 60B11: Probability theory on linear topological spaces
Type
Research Article
Information
Mathematika , Volume 64 , Issue 1 , 2018 , pp. 211 - 229
Copyright
Copyright © University College London 2018 

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