Noncommutative martingale inequalities associated with convex functions
Operator Algebras
2015-09-18 v1 Probability
Abstract
We report recent advances on noncommutative martingale inequalities associated with convex functions. These include noncommutative Burkholder-Gundy inequalities associated with convex functions due to the present authors and Dirksen and Ricard, noncommutative maximal inequalities associated with convex functions due to Os\c{e}kowski and the present authors, and noncommutative Burkholder and Junge-Xu inequalities associated with convex functions due to Randrianantoanina and Lian Wu. Some open problems for noncommutative martingales are also included.
Cite
@article{arxiv.1509.05242,
title = {Noncommutative martingale inequalities associated with convex functions},
author = {Zeqian Chen and Turdebek N. Bekjan},
journal= {arXiv preprint arXiv:1509.05242},
year = {2015}
}
Comments
17 pages, a survey paper. arXiv admin note: substantial text overlap with arXiv:1108.2795