Brownian Forgery of Statistical Dependences

The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences between two statistical systems, and then establish a new B...

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Main Author:	Vincent Wens
Format:	Article
Language:	English
Published:	Frontiers Media S.A. 2018-06-01
Series:	Frontiers in Applied Mathematics and Statistics
Subjects:	Brownian distance covariance Brownian motion nonlinear correlation Levy's forgery theorem statistical independence
Online Access:	https://www.frontiersin.org/article/10.3389/fams.2018.00019/full

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spelling	doaj-bfb11b31f574474bafa5f2b2e0a2e65b2020-11-25T03:23:01ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872018-06-01410.3389/fams.2018.00019378850Brownian Forgery of Statistical DependencesVincent Wens0Vincent Wens1Laboratoire de Cartographie fonctionnelle du Cerveau, ULB Neurosciences Institute, Université libre de Bruxelles, Brussels, BelgiumMagnetoencephalography Unit, Department of Functional Neuroimaging, Service of Nuclear Medicine, CUB – Hôpital Erasme, Brussels, BelgiumThe balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences between two statistical systems, and then establish a new Brownian independence test based on fluctuating random paths. We also argue that this result allows revisiting the theory of Brownian covariance from a physical perspective and opens the possibility of engineering nonlinear correlation measures from more general functional integrals.https://www.frontiersin.org/article/10.3389/fams.2018.00019/fullBrownian distance covarianceBrownian motionnonlinear correlationLevy's forgery theoremstatistical independence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Vincent Wens Vincent Wens
spellingShingle	Vincent Wens Vincent Wens Brownian Forgery of Statistical Dependences Frontiers in Applied Mathematics and Statistics Brownian distance covariance Brownian motion nonlinear correlation Levy's forgery theorem statistical independence
author_facet	Vincent Wens Vincent Wens
author_sort	Vincent Wens
title	Brownian Forgery of Statistical Dependences
title_short	Brownian Forgery of Statistical Dependences
title_full	Brownian Forgery of Statistical Dependences
title_fullStr	Brownian Forgery of Statistical Dependences
title_full_unstemmed	Brownian Forgery of Statistical Dependences
title_sort	brownian forgery of statistical dependences
publisher	Frontiers Media S.A.
series	Frontiers in Applied Mathematics and Statistics
issn	2297-4687
publishDate	2018-06-01
description	The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences between two statistical systems, and then establish a new Brownian independence test based on fluctuating random paths. We also argue that this result allows revisiting the theory of Brownian covariance from a physical perspective and opens the possibility of engineering nonlinear correlation measures from more general functional integrals.
topic	Brownian distance covariance Brownian motion nonlinear correlation Levy's forgery theorem statistical independence
url	https://www.frontiersin.org/article/10.3389/fams.2018.00019/full
work_keys_str_mv	AT vincentwens brownianforgeryofstatisticaldependences AT vincentwens brownianforgeryofstatisticaldependences
_version_	1724608308172554240

Brownian Forgery of Statistical Dependences

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