Syllabus for Math 468, Section G1
This is a special topics course in the theory of Large
Deviations.
Provisional Schedule
- Lecture 1: Some ``Large Deviations'' problems
- Lecture 2: Laplace asymptotics
- Lecture 3: Some definitions and basic results
- Definitions
- Weak LDP's
- Exponential Tightness
- Contraction Principle
- Varadhan's Lemma
- Lecture 4: A simple form of Cramer's Theorem on the real line
- Lecture 5: Schilder's Theorem
- Lecture 6: Fun with Schilder's Theorem
- Lecture 7: Un soupcon d'analyze convexe
- Lecture 8: The Gartner-Ellis theorem
- Lecture 9: Advanced techniques
- Approximate Contraction principles
- Projective Limits
- Lecture 10: Donsker-Varadhan results
References:
- A. Dembo and O. Zeitouni, Large Deviations
Techniques, Jones and Bartlett, 1993.
- J.-D. Deuschel and D. W. Stroock, Large Deviations,
Academic Press, 1989.
- M. I. Freidlin and A. D. Wentzell, Random Perturbations of
Dynamical Systems, Springer, 1984
- D.W. Stroock, An Introduction to the Theory of Large
Deviations, Springer, 1984
- S.R.S. Varadhan, Large Deviations, SIAM, 1984.