Proofs of convergence of random variables

id: proofs-of-convergence-of-random-variables-289-13382992
title: Proofs of convergence of random variables
text: This article is supplemental for “Convergence of random variables” and provides proofs for selected results. Several results will be established using the portmanteau lemma: A sequence {Xn} converges in distribution to X if and only if any of the following conditions are met: E [ f ] → E [ f ] for all bounded, continuous functions f ; E [ f ] → E [ f ] for all bounded, Lipschitz functions f ; lim sup Pr ⁡ ≤ Pr ⁡ for all closed sets C ;
brand slug: wiki
category slug: encyclopedia
description: Variety of proofs provided for the different types of convergence of random variables
original url: https://en.wikipedia.org/wiki/Proofs_of_convergence_of_random_variables
date created:
date modified: 2023-11-15T05:04:59Z
main entity: {"identifier":"Q7250031","url":"https://www.wikidata.org/entity/Q7250031"}
image:
fields total: 13
integrity: 14

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