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Entropic Projections and Dominating Points

Published online by Cambridge University Press:  22 December 2010

Christian Léonard
Christian Léonard*
Affiliation:
Modal-X, Université Paris Ouest, Bât. G, 200 av. de la République, 92000 Nanterre, France; leonard@u-paris10.fr
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Abstract

Entropic projections and dominating points are solutions to convexminimization problems related to conditional laws of largenumbers. They appear in many areas of applied mathematics such asstatistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugateduality and functional analysis, criteria are derived for theexistence of entropic projections, generalized entropicprojections and dominating points. Representations of thegeneralized entropic projections are obtained. It is shown thatthey are the “measure component" of the solutions to someextended entropy minimization problem. This approach leads to newresults and offers a unifying point of view. It also permits toextend previous results on the subject by removing unnecessarytopological restrictions. As a by-product, new proofs of alreadyknown results are provided.

Keywords

Conditional laws of large numbersrandom measureslarge deviationsentropyconvex optimizationentropic projectionsdominating pointsOrlicz spaces
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 343 - 381
Copyright
© EDP Sciences, SMAI, 2010

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