In probability theory, Azuma's inequality or the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose { X k : k = 0 , 1 , 2 , 3 , … } {\displaystyle \{X_{k}:k=0,1,2,3,\dots \}} is a martingale (or super-martingale) and | X k − X k − 1 | ≤ c k , {\displaystyle |X_{k}-X_{k-1}|\leq c_{k},\,} almost surely.
In probability theory, Azuma's inequality or the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose { X k : k = 0 , 1 , 2 , 3 , … } {\displaystyle \{X_{k}:k=0,1,2,3,\dots \}} is a martingale (or super-martingale) and | X k − X k − 1 | ≤ c k , {\displaystyle |X_{k}-X_{k-1}|\leq c_{k},\,} almost surely.
Source: Wikipedia "Azuma's inequality" · CC BY-SA 4.0
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