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2007 | 5 | 1 | 50-83
Tytuł artykułu

Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions

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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.
Opis fizyczny
  • University of Manchester
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