Mathematisches Seminar: Large deviations
Time / location: Tuesday 8 – 10, B 251
First meeting: Tue 13/10/2015 at 10:00 in B 448
(Discussion of topics and assignment of talks)
If you plan to attend the seminar, please register by email until 11/10/2015.
Talks can be given in English or German!
Synopsis
Large deviation theory is a part of probability theory that deals with the dedescription
of events where a sum of random variables deviates from its mean by
more than a "normal" amount, i.e., beyond what is described by the central limit
theorem. A precise calculation of the probabilities of such events turns out to be
crucial for the study of integrals of exponential functional of sums of random variables,
which come up in a variety of different contexts. Large deviation theory
finds application in probability theory, statistics, operations research, ergodic theory,
information theory, statistical physics, financial mathematics, and the list goes on.
[From the preface of den Hollander, see bibliography below]
Prerequisites
Probability theory, Functional analysis (required for more advanced topics)
Audience
Master students of Mathematics, Financial Mathematics and Physics, TMP students
Suggested reading
- A. Dembo, O. Zeitouni, Large deviation techniques and applications, 2nd ed., Springer, New York, 1998.
- F. den Hollander, Large deviations, American Mathematical Society, Providence, RI, 2000.
- J.-D. Deuschel, D. W. Stroock, Large deviations, Academic Press, Boston, 1989.
- F. Rassoul-Agha, T. Seppäläinen, A course on large deviations with an introduction to Gibbs measures, American Mathematical Society, Providence, RI, 2015.
- S. R. S. Varadhan, Large deviations and applications, Soc. f. Industrial a. Appl. Math., Philadelphia, 1984.