AUTHOR=Wens Vincent 

TITLE=Brownian Forgery of Statistical Dependences

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=4

YEAR=2018

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2018.00019

DOI=10.3389/fams.2018.00019

ISSN=2297-4687

ABSTRACT=<p>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.</p>