AM282 - Introduction to Large Deviations (Sp08)
| AM282: Introduction to Large Deviations | ||
|---|---|---|
Lecture 1 (1/24/08) |
What the CLT can tell us about LD, LDP, Cramer's Theorem and examples | |
| Lecture 2 (1/29/08) | Varadhan's Lemma and Proof, Laplace Principle, Mogulski's Example, Contraction Princple | |
| Lecture 3 (1/31/08) | Conditioning Interpretation, Mogulski revisted, Uniquness of rate function, Super-exponentials, Example of Stoch. Recursive Eqn. | |
| Lecture 4 (2/5/08) | Convex Functions and the Legendre Tranform | |
| Lecture 5 (2/7/08) | More on the Legendre Tranform, Proof of Cramer's Theorem (lower bound) | |
| Lecture 6 (2/12/08) | Proof of Cramer's Theorem (upper bound), Example usng Moguskii's Theorem | |
| Lecture 7 (2/14/08) | Large Deviations and Viscosity Solutionss: Intro, principle of optimality, examples, sub and super solutions | |
| Lecture 8-9 (2/21-26/08) | Viscosity Solutions: Comparison Principle, connection to the rate function | |
| Lecture 10 (3/4/08) | Viscosity Solutions continued... | |
| Lecture 11 (3/6/08) | Random vector fields, examples - tracking loops and related devices, review of convergence in distribution, intro to relative entropy | |
| Lecture 12 (3/11/08) | Relative entropy: alternative definition, chain rule | |
| Lecture 13 (3/13/08) | Relative entropy: functionals of iid sequences, tie to LDP, Sanov's theorem (empirical measures) | |
| Lecture 14 (3/18/08) | LDP for empirical measures (Sanov's Theorem) | |
| Lecture 15 (3/20/08) | Tau topology, Intro to empirical measure LDP for stationary Markov Process | |
| Lecture 16 (4/1/08) | Empirical Measure of a Markov Chain continued..., Intro to Friedlin Wentsell Theory | |
| Lecture 17 (4/3/08) | Large time behavior for Friedlin-Wentsell Theory, model for discussion | |
| Lecture 18 (4/8/08) | Large time behavior for Friedlin-Wentsell Theory continued... | |
| Lecture 19 (4/10/08) | Mean escape time for Friedlin-Wentsell theory | |