Comparaison de mesures gaussiennes et de mesures produit
type: Item
instance of: scholarly article
title: Comparaison de mesures gaussiennes et de mesures produit
zbMATH Open document ID: 0536.60047
author: Xavier Fernique
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1984-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77230
review text: The author proves the following: let \(\xi =(\xi_ i)\), \(\eta =(\eta_ i)\) be two random variables with values in \({\mathbb{R}}^{\infty}={\mathbb{R}}\times {\mathbb{R}}\times..\). such that \(\xi\) is Gaussian, the \(\eta_ i's\) are independent and law \((\xi_ i)\) equivalent to law \((\eta_ i)\), \(i=1,2,...\); then the following are equivalent: (i) law (\(\xi)\) is not orthogonal to law (\(\eta)\); (ii) law (\(\xi)\) is equivalent to law (\(\eta)\); (iii) law (\(\xi)\) and law (\(\eta)\) are equivalent to the product measure \(\otimes_ i\) law \((\xi_ i)\). Besides the intrinsic interest of the theorem, the technique of proof used is significant.
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 3852133
zbMATH Keywords: marginal distributions
zbMATH Keywords: Gaussian measure
zbMATH Keywords: product measure
zbMATH Keywords: Hellinger distance
reviewed by: Srishti D. Chatterji
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3852133