A Systematic Martingale Construction with Applications to Permutation Inequalities
Probability
2012-10-30 v1
Abstract
We illustrate a process that constructs martingales from raw material that arises naturally from the theory of sampling without replacement.The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by A. Garsia in the study of rearrangement of orthogonal series.
Keywords
Cite
@article{arxiv.1210.7503,
title = {A Systematic Martingale Construction with Applications to Permutation Inequalities},
author = {Vladimir Pozdnyakov and J. Michael Steele},
journal= {arXiv preprint arXiv:1210.7503},
year = {2012}
}