Azuma–Hoeffding inequality

Target entity: Azuma–Hoeffding inequality
Context triple: [Bernstein inequalities, relatedTo, Azuma–Hoeffding inequality]

• A. Chernoff bound
  The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.
• B. Chebyshev inequalities
  Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
• C. Bennett inequality
  Bennett inequality is a probabilistic bound that provides exponential tail estimates for sums of independent random variables, refining classical concentration inequalities like Bernstein’s.
• D. Berry–Esseen theorem
  The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
• E. Doob’s maximal inequalities
  Doob’s maximal inequalities are fundamental results in probability theory that provide bounds on the maximum value of a martingale or submartingale in terms of its expected terminal value, playing a key role in convergence and limit theorems.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Azuma–Hoeffding inequality
Target entity description: The Azuma–Hoeffding inequality is a concentration inequality that bounds the probability of large deviations for martingales with bounded differences, generalizing Hoeffding’s inequality to dependent sequences.

• A. Chernoff bound
  The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.
• B. Chebyshev inequalities
  Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
• C. Bennett inequality
  Bennett inequality is a probabilistic bound that provides exponential tail estimates for sums of independent random variables, refining classical concentration inequalities like Bernstein’s.
• D. Berry–Esseen theorem
  The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
• E. Doob’s maximal inequalities
  Doob’s maximal inequalities are fundamental results in probability theory that provide bounds on the maximum value of a martingale or submartingale in terms of its expected terminal value, playing a key role in convergence and limit theorems.
• F. None of above. chosen