**Seminar in
Large Deviations – Spring 2010**

**Announcements**

Dmitry Kramkov will be giving the seminar on Thursday, February 4. He will be giving a review on weak convergence of measures and dicussing the connections between weak convergence and LDP.

**Basic Class Information**

**Time : **Thursdays
from 4:30 to 6:30 PM

**Room : **Wean
Hall 6423

**Lectures**

**Lecture 1
– January 21, 2010 – Introduction/Cramer's Theorem**

Assigned Exercises – Due February 4, 2010

__Example
of a weak but not full LDP__

It was asked if every exponentially tight sequence of measures on a Polish space contains a subsequence which satisfies a LDP with good rate function I. This is in fact true and is proved as Theorem 1.3.7 (page 26) in the Dupuis and Ellis book.

**Lecture 2 – January 28, 2010 – Cramer's Theorem**

Assigned Exercises – Due February 11, 2010

Answers to some questions raised in Office Hours

**Lecture 3 – February 4, 2010 – Review of Weak Convergence**

No Assigned Exercises

**Lecture
4 – February 11, 2010 – Applications of Cramer's Theorem and the
Gartner Ellis Theorem**

Assigned Exercises- Due February 25, 2010

**Lecture 5 – February 18, 2010 – The Gartner Ellis Theorem**

__Assigned
Exercies – Due March 4, 2010__

**Lecture 6 – February 25, 2010 – Varadhan's Integral Lemma**

__Assigned
Exercises – Due March 18, 2010__

**Lecture 7 – March 4, 2010 – Existence Results, Contraction and
Approximate Contraction Principles**

__Assigned
Exercices - Due March 18, 2010__

**Lecture 8 – March 18, 2010 - Sample path LDP : Mogulskii's and
Schilder's Theorems**

__Assigned
Exercises - Due April 1, 2010__

**Lecture 9 – March 25, 2010 – Hypothesis Testing with an
application to Wireless Sensor Networks**

No Assigned Exercises

**Lecture 10 – April 1, 2010 – Mogulskii's Theorem,
Freidlin-Wentzell Theory.**

__Assigned
Exercises - Due April 15, 2010__

**Lecture 11 – April 8, 2010 – Occupancy Time LDP for ergodic
Markov Processes I – Finite State Space Markov Chains**

Assigned Exercises - Due April 22, 2010

**Lecture 12 – April 15, 2010 – Occupancy Time LDP for ergodic
Markov Processes II – Markov Chains with General State Spaces**

Assigned Exercises - Due April 29, 2010

**Lecture
13 – April 22, 2010 – Asymptotically Optimal Importance Sampling
with Explicit Formulas in Continuous Time**

No Assigned Exercises

**Lecture
14 – April 29, 2010 – Occupancy Time LDP for ergodic Markov
Processes III – Continuous time processes with a focus on one
dimensional diffusions. **

No Assigned Exercises