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On Cramér's Theory in Infinite Dimensions

Raphaël Cerf
Publisher: 
Société Mathématique de France
Publication Date: 
2007
Number of Pages: 
159
Format: 
Paperback
Series: 
Panoramas et Sybthèses 23
Price: 
53.00
ISBN: 
978-2-85629-235-8
Category: 
Monograph
We do not plan to review this book.
  • 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 Log-Laplace
  • $I=\Lambda^\ast$: the discrete case
  • $I=\Lambda^\ast$: the smooth case
  • $I=\Lambda^\ast$: the finite dimensional case
  • $I=\Lambda^\ast$: the finite 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
Tags: 
Stochastic Processes
Statistical Mechanics
Probability Theory
Functional Analysis