Brownian forgery of statistical dependences
Abstract
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.
Cite
@article{arxiv.1705.01372,
title = {Brownian forgery of statistical dependences},
author = {Vincent Wens},
journal= {arXiv preprint arXiv:1705.01372},
year = {2018}
}
Comments
13 pages, 2 figures, formatting based on revtex4; v2: revised proof of extended forgery and minor changes; v3: additional discussion on practical implementation and minor edits, published version