Abstract
We establish an Azuma type inequality under a Lipshitz condition for martingales in the framework of noncommutative probability spaces and apply it to deduce a noncommutative Heoffding inequality as well as a noncommutative McDiarmid type inequality. We also provide a noncommutative Azuma inequality for noncommutative supermartingales in which instead of a fixed upper bound for the variance we assume that the variance is bounded above by a linear function of variables. We then employ it to deduce a noncommutative Bernstein inequality and an inequality involving $L_{p}$-norm of the sum of a martingale difference.
Citation
Ghadir Sadeghi. Mohammad Sal Moslehian. "Noncommutative martingale concentration inequalities." Illinois J. Math. 58 (2) 561 - 575, Summer 2014. https://doi.org/10.1215/ijm/1436275498
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