Brownian Forgery of Statistical Dependences

Frontiers in Applied Mathematics and Statistics

Vincent Wens² 

[1] Laboratoire de Cartographie fonctionnelle du Cerveau, ULB Neurosciences Institute, Université libre de Bruxelles, Brussels, Belgium;Magnetoencephalography Unit, Department of Functional Neuroimaging, Service of Nuclear Medicine, CUB – Hôpital Erasme, Brussels, Belgium;

关键词: Brownian distance covariance;    Brownian motion;    nonlinear correlation;    Levy's forgery theorem;    statistical independence;   

DOI  :  10.3389/fams.2018.00019

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown