On Cramer's theory in infinite dimensions / Raphael Cerf

Auteur principal : Cerf, Raphaël, AuteurType de document : MonographieCollection : Panoramas et synthèses, 23Langue : anglais.Pays: France.Éditeur : Paris : Société Mathématique de France, 2007Description : 1 vol. (VI-159 p.) ; 24 cmISBN: 9782856292358.ISSN: 1272-3835.Bibliographie : Bibliogr. p. [155]-159. Index.Sujet MSC : 60F10, Limit theorems in probability theory, Large deviations
46A03, Functional analysis - Topological linear spaces and related structures, General theory of locally convex spaces
49J35, Existence theories in calculus of variations and optimal control, Existence of solutions for minimax problems
En-ligne : Sommaire Item type: Monographie
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This slim monography is a self-contained account on Cramér's theory in infinite dimensions. It is mainly based on the classical texts of R. Azencott [Lect. Notes Math. 774 (1980; Zbl 0435.60028)], R. R. Bahadur and S. L. Zabell [Ann. Probab. 7, 587–621 (1979; Zbl 0424.60028)], A. Dembo and O. Zeitouni [“Large deviation techniques and applications”. 2nd ed. (1998; Zbl 0896.60013)] and J.-D. Deuschel and D. W. Stroock [“Large deviations” (1989; Zbl 0705.60029)]. However the focus of this text lies on the topological assumptions in order to carry out the heart of the theory in greatest generality, especially without a priori necessity to work in Polish spaces and their Borel-σ field. This is the reason why it considerably appeals to functional analytic tools coming from the theory of locally convex vector spaces, which for the convenience of the reader are entirely gathered here. (Zentralblatt)

Bibliogr. p. [155]-159. Index

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