Cramér's theorem in measurable locally convex spaces

Details Cramér's theorem in measurable locally convex spaces Cramér's theorem in measurable locally convex spaces

2011-03-22

arxiv.org/abs/1103.4416v1

Mathematics

Probability

38 pages, in french

Scientific paper

We give a general setting for Cram\'er's large deviations theorem for the empirical means of a sequence of i.i.d. random vectors, which contains Cram\'er's theorem in a Banach space and Sanov's theorem. ----- Nous \'etablissons un cadre g\'en\'eral pour le th\'eor\`eme de Cram\'er sur les grandes d\'eviations des moyennes empiriques d'une suite de vecteurs al\'eatoires i.i.d., cadre qui contient le th\'eor\`eme de Cram\'er dans les espaces de Banach s\'eparables et le th\'eor\`eme de Sanov.

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