Itô–Nisio theorem
id:
it-nisio-theorem-276-8123169
title:
Itô–Nisio theorem
text:
The Itô-Nisio theorem is a theorem from probability theory that characterizes convergence in Banach spaces. The theorem shows the equivalence of the different types of convergence for sums of independent and symmetric random variables in Banach spaces. The Itô-Nisio theorem leads to a generalization of Wiener's construction of the Brownian motion. The symmetry of the distribution in the theorem is needed in infinite spaces. The theorem was proven by Japanese mathematicians Kiyoshi Itô and Makiko
brand slug:
wiki
category slug:
encyclopedia
description:
Convergence of random variables in Banach spaces
original url:
https://en.wikipedia.org/wiki/It%C3%B4%E2%80%93Nisio_theorem
date created:
date modified:
2023-08-13T08:52:42Z
main entity:
{"identifier":"Q113623203","url":"https://www.wikidata.org/entity/Q113623203"}
image:
fields total:
13
integrity:
14