Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative Chernoff bounds has, to our knowledge, never been explicitly formulated. We formulate a multiplicative-error version of Azuma's inequality. We then show how to apply this new inequality in order to greatly simplify (and correct) the analysis of contention delays in multithreaded systems managed by randomized work stealing.

翻译：Azuma的不平等是证明随机变量的集中界限的工具。 这种不平等可以被视为添加的 Chernoff 边框的自然概括。 另一方面,据我们所知,对倍增的 Chernoff 边框的类似普遍化从未明确阐述过。 我们对Azuma的不平等进行了多倍化的描述。 然后,我们展示了如何应用这种新的不平等,以便大大简化(并纠正)对通过随机性工作偷盗管理的多读系统中争议拖延的分析。