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January, 1994 On a Domination of Sums of Random Variables by Sums of Conditionally Independent Ones
Pawel Hitczenko
Ann. Probab. 22(1): 453-468 (January, 1994). DOI: 10.1214/aop/1176988868

Abstract

It is known that if $(X_n)$ and $(Y_n)$ are two $(\mathscr{F}_n)$-adapted sequences of random variables such that for each $k \geq 1$ the conditional distributions of $X_k$ and $Y_k$, given $\mathscr{F}_{k-1}$, coincide a.s., then the following is true: $\|\sum X_k\|_p \leq B_p\| \sum Y_k\|_p, 1 \leq p < \infty$, for some constant $B_p$ depending only on $p$. The aim of this paper is to show that if a sequence $(Y_n)$ is conditionally independent, then the constant $B_p$ may actually be chosen to be independent of $p$. This significantly improves all hitherto known estimates on $B_p$ and extends an earlier result of Klass on randomly stopped sums of independent random variables as well as our recent result dealing with martingale transforms of Rademacher sequences.

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Pawel Hitczenko. "On a Domination of Sums of Random Variables by Sums of Conditionally Independent Ones." Ann. Probab. 22 (1) 453 - 468, January, 1994. https://doi.org/10.1214/aop/1176988868

Information

Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0809.60022
MathSciNet: MR1258886
Digital Object Identifier: 10.1214/aop/1176988868

Subjects:
Primary: 60E15
Secondary: 60G42

Keywords: martingale , Moment inequalities , tangent sequences

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • January, 1994
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