Panoramas et Synthèses 2007; 159 pp; softcover Number: 23 ISBN10: 2856292356 ISBN13: 9782856292358 List Price: US$53 Member Price: US$42.40 Order Code: PASY/23
 This text is a selfcontained account of Cramér's theory in infinite dimensions. The point of view is slightly different from the classical texts of Azencott, Bahadur and Zabell, Dembo and Zeitouni, and Deuschel and Stroock. The authors have been trying to understand the relevance of the topological hypotheses necessary to carry out the core of the theory. They have also drawn some inspiration from the analogy between the large deviation proofs in statistical mechanics and for i.i.d. random variables. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicans interested in probability and analysis. Table of Contents  Introduction
 Large deviation theory
 Topological vector spaces
 The model
 The weak large deviation principle
 The measurability hypotheses
 Subadditivity
 Proof of Theorem 5.2
 Convex regularity
 Enhanced upper bound
 The Cramér transform \(I(\mu, A)\) as a function of \(\mu\)
 The Cramér transform and the LogLaplace
 \(I=\Lambda^\ast\): the discrete case
 \(I=\Lambda^\ast\): the smooth case
 \(I=\Lambda^\ast\): the finite dimensional case
 \(I=\Lambda^\ast\): the infinite dimensions
 Exponential tightness
 Cramér's theorem in \(\mathbb R\)
 Cramér's theorem in \(\mathbb R^d\)
 Cramér's theorem in the weak topology
 Cramér's theorem in a Banach space
 Gaussian measures
 Sanov's theorem: autonomous derivation
 Cramér's theorem implies Sanov's theorem
 Sanov's theorem implies the compact Cramér theorem
 Mosco convergence
 A. Lusin's theorem
 B. The mean of a probability measure
 C. Ky Fan's proof of the minimax theorem
 Index
 Bibliography
