Date of this Version
Journal of Mathematical Analysis and Applications
We illustrate a process that constructs martingales with help from matrix products that arise naturally in 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.
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Construction of martingales, permutation inequalities, garsia inequality, combinatorial martingales; Discrete Brownian bridge
Pozdnyakov, V., & Steele, J. M. (2013). A Systematic Martingale Construction With Applications to Permutation Inequalities. Journal of Mathematical Analysis and Applications, 407 (1), 130-140. http://dx.doi.org/10.1016/j.jmaa.2013.05.010
Date Posted: 27 November 2017
This document has been peer reviewed.