We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the topological character of the results makes them stable under small perturbations, which is important for applications in models of stochastic processes.
@article{bwmeta1.element.doi-10_2478_s11533-006-0034-5,
author = {Khadiga Arwini and Christopher Dodson},
title = {Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {50-83},
zbl = {1126.53010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0034-5}
}
Khadiga Arwini; Christopher Dodson. Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions. Open Mathematics, Tome 5 (2007) pp. 50-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0034-5/
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