# Noncommutative Blackwell-Ross martingale inequality

## TL;DR

This paper extends classical martingale inequalities to the noncommutative setting, providing new bounds for supermartingales and deriving an Azuma-type inequality.

## Contribution

It introduces a noncommutative Blackwell-Ross inequality for supermartingales, generalizing previous work to the noncommutative framework.

## Key findings

- Established a noncommutative Blackwell-Ross inequality for supermartingales.
- Derived an Azuma-type inequality from the new bounds.
- Generalized classical martingale inequalities to noncommutative probability.

## Abstract

We establish a noncommutative Blackwell--Ross inequality for supermartingales under a suitable condition which generalize Khan's works to the noncommutative setting. We then employ it to deduce an Azuma-type inequality.