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Graduate Course "Large deviation theory and applications"
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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 recent award of the Abel prize to S.R.S. Varadhan,
one of the pioneers of the subject. The subject is intimately related to combinatorial
theory and the calculus of variations. Applications of large deviation theory arise,
for example, in statistical mechanics, information theory and insurance.
In the course I will present the basic principles of large deviation theory
using the easiest set up of independent, identically distributed sequences
wherever possible. Later some more advanced examples and applications
will be discussed and participants will get the opportunity to contribute talks.
The current draft of the course looks like this:
- Lecture 1: Cramer's theorem and the moderate deviation principle
- Lecture 2: Framework and basics of large deviations
- Lecture 3: Large deviations from combinatorics: The method of types and Sanov's theorem for empirical measures
- Lecture 4: Large deviations from probability: The change of measure technique and Sanov's theorem for empirical pair measures
- Lecture 5: Process level large deviations and the Dawson-Gärtner theorem
- Lecture 6: Varadhan's lemma and its inverse
- Lecture 7: Applications 1:
The parabolic Anderson model.
Speaker: Marcel Ortgiese.
- Lecture 8: Applications 2:
The theorem of Bahadur and Rao and large portfolio losses.
Speaker: Martin Herdegen.
- Lecture 9: Applications 3: Branching processes.
Speaker: Andreas Kyprianou.
Here is the final draft of my lecture notes.
Prerequisites for the course are an undergraduate course in probability
of about third year level and good personal motivation.
The course is scheduled for Mondays 15:15 to 17:05 in 2E3.5.
Last changed on 13.11.2008.
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