Hinweis: Diese Veranstaltung wird im Wintersemester 2013/14 in englischer Sprache durchgeführt. Das betrifft insbesondere die Vorlesung sowie die Hausaufgaben. Aus diesem Grund stellen wir fast alle Informationen nur in englischer Sprache zur Verfügung.

Large Deviations in winter term 2013/14

Lecture:
Dates:Wednesdays, 08:15 to 09:45 in room 3.1.08 (Hochbrück-Seminarraum 1, 3rd floor, 8102.03.108) at Parkring 37 (entrance to the right of EDEKA) in Garching-Hochbrück.
Start: 16th October 2013
Instructor:Prof. Dr. Noam Berger
Prerequisites:

Probability Theory
A link to the lecture notes of Prof. Gantert's lecture is available here.

Content:

Large deviation theory is a part of probability theory which deals with the description of "unlikely" events and determines how fast their probabilities decay. The rate of decay turns out to be crucial in determining optmal shapes of random paths under consideration. This principle also leads to the study the integrals of exponential functionals of sums of random variables, which come up in many different contexts, in and outside mathematics. Large deviation theory finds applications in statistical mechanics, ergodic theory, information theory, statistics and financial mathematics.

The course will treat large deviations for i.i.d. sequences and Markov chains, large deviations for empirical measures and for sample paths and the Gibbs conditioning principle.

Literature:

Amir Dembo, Ofer Zeitouni: Large Deviations Techniques and Applications,
Springer (1998).

Frank den Hollander: Large Deviations,
Fields Institute Monographs (2002).

Current years lecture notes here!

Final exam:
Assessment regime:

Written exam: Wednesday, 19.2.14, 13:00-14:00, Hochbrück Hörsaal 1,8102 eg 116, 0.01.16

Second Written exam: Friday, 4.4.2014, 10:30-11:30, Hochbrück Hörsaal 1, 8102 eg 116, 0.01.16

If you have any questions concerning the exercise classes, please contact Dr. Chiranjib Mukherjee.