Entropic Projections and Dominating Points

Christian Léonard (1)

1 MODAL'X - Modélisation aléatoire de Paris X

Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for their existence. Representations of the generalized entropic projections are obtained: they are the ``measure component" of some extended entropy minimization problem.

Mots clés: Conditional laws of large numbers; random measures; large deviations; entropy; convex optimization; entropic projections; dominating points

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Christian Léonard. Entropic Projections and Dominating Points. ESAIM: Probability and Statistics, 2010, 14, pp.343-381. ⟨10.1051/ps/2009003⟩. ⟨hal-00184785v2⟩