Azuma's Inequality, also called the Azuma-Hoeffding Inequality, is a concentration inequality bounding how far a martingale with bounded increments can stray from its starting value after a given number of steps, showing the probability of a large deviation falls off exponentially as the deviation grows. Named for Kazuoki Azuma and Wassily Hoeffding, it is a foundational tool of probability theory used throughout combinatorics and theoretical computer science to prove that quantities built from many small, weakly dependent random choices concentrate tightly around their expected value.
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StatementGives a concentration result for the values of martingales that have bounded differences, bounding P(X_N - X_0 >= epsilon) by exp(-epsilon^2 / (2 sum of c_k^2)). 2 Classification
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Source Azuma's inequality (Wikipedia)
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Source Azuma's inequality (Wikipedia)
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1. Wikipedia: Azuma's inequality
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
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.
2. Azuma's inequality (Wikipedia)
Introduction, sentence 1
gives a concentration result for the values of martingales that have bounded differences
In Branch: Probability and Statistics, Lead sentence
In probability theory, Azuma's inequality or the Azuma-Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) give
Proved By: Wassily Hoeffding, Lead paragraph
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
In Group: Probability Theory, Lead section
In probability theory, Azuma's inequality or the Azuma-Hoeffding inequality
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