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:
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image:
fields total:
13
integrity:
14