normalized version of the sample mean converges to a standard normal distribution. This holds even if the original variables themselves are not normally distributed...

{\displaystyle (2)} below, subgaussian random variables can be characterized as those random variables with finite subgaussian norm. If there exists some...

Cf. N. Bouleau, F. Hirsch, Formes de Dirichlet générales et densité des variables aléatoires réelles sur l'espace de Wiener, Journal of Functional Analysis...

(1936). [Reference given in Dover book] P. Levy, Théorie de l'addition des variables aléatoires, Paris, 1937, p. 320. Ergodic Theory with Applications to...

statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of only 3 possible distribution...

independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable...

1951. Sur la convergence presque complète des moyennes de variables aléatoires, 273 pages, Paris, Institut de statistique de l'université de Paris, 1957...

des variables aléatoires les plus indépendantes" [Search for the most independent random variables], Comptes rendus hebdomadaires des séances de l'Académie...

{1}{\sqrt {n}}}G_{n}} converges in distribution to a random real tree, which we call a Brownian tree. Here, the limit used is the convergence in distribution...

Boiteux, M (1951). "La tarification au coût marginal et les demandes aléatoires". Cahiers du Séminaire d'Économétrie. 1 (1): 56–69. doi:10.2307/20075348...