Burkholder–Davis–Gundy inequalities

Target entity: Burkholder–Davis–Gundy inequalities
Context triple: [Itô isometry, relatedTo, Burkholder–Davis–Gundy inequalities]

• A. 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.
• B. Clark–Ocone formula
  The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
• C. G-Brownian motion
  G-Brownian motion is a generalization of classical Brownian motion developed within the framework of sublinear expectations to model uncertainty in volatility.
• D. Feynman–Kac formula
  The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
• E. Lyons' rough path theory
  Lyons' rough path theory is a mathematical framework that extends classical calculus to analyze and solve differential equations driven by highly irregular signals, such as paths with low regularity or stochastic processes like Brownian motion.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Burkholder–Davis–Gundy inequalities
Target entity description: The Burkholder–Davis–Gundy inequalities are fundamental results in stochastic analysis that provide two-sided bounds relating the moments of martingales to the moments of their quadratic variation.

• A. 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.
• B. Clark–Ocone formula
  The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
• C. G-Brownian motion
  G-Brownian motion is a generalization of classical Brownian motion developed within the framework of sublinear expectations to model uncertainty in volatility.
• D. Feynman–Kac formula
  The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
• E. Lyons' rough path theory
  Lyons' rough path theory is a mathematical framework that extends classical calculus to analyze and solve differential equations driven by highly irregular signals, such as paths with low regularity or stochastic processes like Brownian motion.
• F. None of above. chosen