Donsker's invariance principle

Target entity: Donsker's invariance principle
Context triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Donsker's invariance principle]

• A. 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.
• B. Khinchin's law of the iterated logarithm
  Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
• C. Lyapunov central limit theorem
  The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
• D. Lindeberg–Feller central limit theorem
  The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
• E. Lévy’s continuity theorem
  Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Donsker's invariance principle
Target entity description: Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.

• A. 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.
• B. Khinchin's law of the iterated logarithm
  Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
• C. Lyapunov central limit theorem
  The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
• D. Lindeberg–Feller central limit theorem
  The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
• E. Lévy’s continuity theorem
  Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
• F. None of above. chosen