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In probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker, is a functional extension of the central limit theorem. Let be a sequence of independent and identically distributed (i.i.d.) random variables with mean 0 and variance 1. Let . The stochastic process is known as a random walk. Define the diffusively rescaled random walk (partial-sum process) by

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rdfs:label	Teorema de Donsker (ca) Satz von Donsker (de) Donsker's theorem (en) Théorème de Donsker (fr) Teorema de Donsker (pt)
rdfs:comment	Der Satz von Donsker ist ein fundamentaler Satz aus der Stochastik, genauer aus der Theorie der stochastischen Prozesse. Der Satz begründet die Existenz des Wiener-Maßes bzw. der Brownschen Bewegung und bietet zugleich eine Konstruktionsmöglichkeit. Das Theorem ist die funktionale Variante des zentralen Grenzwertsatzes und ist deshalb auch unter dem Namen Funktionaler Grenzwertsatz und Donskersches Invarianzprinzip bekannt. Er wurde 1952 vom amerikanischen Mathematiker Monroe D. Donsker bewiesen. (de) En théorie des probabilités, le théorème de Donsker établit la convergence en loi d'une marche aléatoire vers un processus stochastique gaussien. Il est parfois appelé le théorème central limite fonctionnel. Ce théorème est une référence pour la convergence en loi de marches aléatoires renormalisées vers un processus à temps continus. De nombreux théorèmes sont alors dits de « type Donsker ». (fr) Em teoria da probabilidade, o teorema de Donsker (também conhecido como princípio da invariância de Donsker, ou teorema central do limite funcional), em homenagem ao matemático Monroe D. Donsker, é uma extensão funcional do teorema central do limite. (pt) En teoria de probabilitat, el teorema de Donsker (també conegut com principi d'invariància de Donsker, o teorema del límit central funcional), que du el nom de Monroe D. Donsker, és una extensió funcional del teorema del límit central. Sigui una seqüència de variables aleatòries independents i idènticament distribuïdes (i.i.d.) amb mitjana 0 i variància 1. Sigui Es coneix com al procés estocàstic . Defineixi's la ruta alelatòria escalada difusivament (procés de suma parcial) com (ca) In probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker, is a functional extension of the central limit theorem. Let be a sequence of independent and identically distributed (i.i.d.) random variables with mean 0 and variance 1. Let . The stochastic process is known as a random walk. Define the diffusively rescaled random walk (partial-sum process) by (en)
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dcterms:subject	Probability theorems Theorems in statistics Empirical process
Wikipage page ID	3828419 (xsd:integer)
Wikipage revision ID	1046693575 (xsd:integer)
Link from a Wikipage to another Wikipage	Monroe D. Donsker Converges in distribution Probability theorems Càdlàg Uniform distribution (continuous) Continuous function Convergence in probability Empirical distribution function Gaussian process Skorokhod space Function space Central limit theorem Normal distribution Glivenko–Cantelli theorem Kolmogorov–Smirnov test Komlós–Major–Tusnády approximation Gaussian random variable Probability theory Random variable Theorems in statistics Weak convergence of measures Wiener process Convergence in distribution Independent and identically distributed random variables Brownian bridge Empirical process Random walk
sameAs	Donsker's theorem Donsker's theorem Donsker's theorem Donsker's theorem Donsker's theorem Donsker's theorem Donsker's theorem Donsker's theorem
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has abstract	En teoria de probabilitat, el teorema de Donsker (també conegut com principi d'invariància de Donsker, o teorema del límit central funcional), que du el nom de Monroe D. Donsker, és una extensió funcional del teorema del límit central. Sigui una seqüència de variables aleatòries independents i idènticament distribuïdes (i.i.d.) amb mitjana 0 i variància 1. Sigui Es coneix com al procés estocàstic . Defineixi's la ruta alelatòria escalada difusivament (procés de suma parcial) com El teorema del límit central afirma que convergeix en distribució a una variable aleatòria gaussiana estàndard a mesura que . El principi d'invariància de Donsker estén aquesta convergència a la funció sencera . Més concretament, en la seva forma moderna, el principi d'invariància de Donsker afirma que: com que les variables aleatòries prenen valors en l'espai de Skorokhod , la funció aleatòria convergeix en distribució al moviment brownià estàndard a mesura que (ca) Der Satz von Donsker ist ein fundamentaler Satz aus der Stochastik, genauer aus der Theorie der stochastischen Prozesse. Der Satz begründet die Existenz des Wiener-Maßes bzw. der Brownschen Bewegung und bietet zugleich eine Konstruktionsmöglichkeit. Das Theorem ist die funktionale Variante des zentralen Grenzwertsatzes und ist deshalb auch unter dem Namen Funktionaler Grenzwertsatz und Donskersches Invarianzprinzip bekannt. Er wurde 1952 vom amerikanischen Mathematiker Monroe D. Donsker bewiesen. (de) In probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker, is a functional extension of the central limit theorem. Let be a sequence of independent and identically distributed (i.i.d.) random variables with mean 0 and variance 1. Let . The stochastic process is known as a random walk. Define the diffusively rescaled random walk (partial-sum process) by The central limit theorem asserts that converges in distribution to a standard Gaussian random variable as . Donsker's invariance principle extends this convergence to the whole function . More precisely, in its modern form, Donsker's invariance principle states that: As random variables taking values in the Skorokhod space , the random function converges in distribution to a standard Brownian motion as (en) En théorie des probabilités, le théorème de Donsker établit la convergence en loi d'une marche aléatoire vers un processus stochastique gaussien. Il est parfois appelé le théorème central limite fonctionnel. Ce théorème est une référence pour la convergence en loi de marches aléatoires renormalisées vers un processus à temps continus. De nombreux théorèmes sont alors dits de « type Donsker ». (fr) Em teoria da probabilidade, o teorema de Donsker (também conhecido como princípio da invariância de Donsker, ou teorema central do limite funcional), em homenagem ao matemático Monroe D. Donsker, é uma extensão funcional do teorema central do limite. (pt)
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is Link from a Wikipage to another Wikipage of	Monroe D. Donsker List of probability topics Gaussian free field Convergence of Probability Measures Empirical process Glivenko–Cantelli theorem Kolmogorov–Smirnov test Wiener process Brownian bridge Brownian motion Brownian web Catalog of articles in probability theory Random walk List of statistics articles List of theorems Scaling limit Stochastic process Donsker theorem Donsker’s theorem
is Wikipage redirect of	Donsker theorem Donsker’s theorem

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