Journal article
On a Domination of Sums of Random Variables by Sums of Conditionally Independent Ones
The Annals of probability, v 22(1), pp 453-468
01 Jan 1994
Abstract
It is known that if (Xn) and (Yn) are two (Fn)-adapted sequences of random variables such that for each k ≥ 1 the conditional distributions of Xkand Yk, given Fk-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 Bpdepending only on p. The aim of this paper is to show that if a sequence (Yn) is conditionally independent, then the constant Bpmay actually be chosen to be independent of p. This significantly improves all hitherto known estimates on Bpand 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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Details
- Title
- On a Domination of Sums of Random Variables by Sums of Conditionally Independent Ones
- Creators
- Pawel Hitczenko
- Publication Details
- The Annals of probability, v 22(1), pp 453-468
- Publisher
- Institute of Mathematical Statistics
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1994NB20600024
- Other Identifier
- 991020532108204721
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- Web of Science research areas
- Statistics & Probability