Large deviation theory deals with the decay of the probability of increasingly
unlikely events. It is one of the key techniques of modern probability, a role
which is emphasised by the award of the 2007 Abel prize to S.R.S. Varadhan,
one of the pioneers of the subject. A relatively recent approach to this theory
is based on the analogy to weak convergence of probability measures and was developed by
Puhalskii, O'Brien and Vervaat, de Acosta and others. We base our study of the method
on the recent book by Feng and Kurtz `Large deviations for stochastic processes'.
Graduate Course "Weak convergence methods for large deviations"
In the course I will use the first three lectures to present background and basic
principles of large deviation theory. Then the participants take over and present the
core material of the book (Chapters 5 to 8) and a selection of examples (Chapter 9 to 13).
Here is a provisional schedule:
- Lecture 1 (Oct 6): Introduction to large deviations I
- Lecture 2 (Oct 13): Introduction to large deviations II
- Lecture 3 (Oct 20): Introduction to large deviations III
- Lecture 4 (Nov 3rd): Large deviations for Markov processes and nonlinear semigroup convergence (Chapter 5)
- Lecture 5 (Nov 10th): Large deviations and nonlinear semigroup convergence using viscosity solutions (Chapter 6)
- Lecture 6 (Nov 17th): Extension of viscosity solution methods (Chapter 7)
- Lecture 7 (Nov 24th): The Nisio semigroup and a control representation of the rate function (Chapter 8)
- Lecture 8 (Dec 1st): Example I: Small perturbation problems (Chapter 10)
- Lecture 9 (Dec 15th): Example II: Random evolutions (Chapter 11)
We will provide copies of the relvant sections of the book to those presenting lectures. Lecture notes
for the first three lectures are available here to
Further material for self-study:
Here is are lecture notes of a graduate course I gave in 2008 presenting
a short introduction to large deviations . This is different from the introduction I give in the first three lectures,
mostly as it contains additional material and motivation.
An introduction to viscosity solutions by Federica Dragoni can be found here
An undergraduate course in measure-theoretic probability
and good personal motivation.
The course is scheduled for Wednesdays 10:15 to 12:05 in 4W1.7.
Last changed on 8.10.2010.
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