Hinweis: Diese Veranstaltung wird im Wintersemester 2015/16 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 2015/16

Lecture:
Dates:Wednesdays, 08:15 to 09:45 in room BC2 3.5.06 (Hochbrück-Seminarraum 3, 3rd floor, 8102.03.506) at Parkring 37 (entrance to the right of EDEKA) in Garching-Hochbrück.
Start: 14th October 2015
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).

Exercises

Exercise classes:
Dates of classes:

Wednesdays, 12:15 to 13:45 in room 0.01.04 (Seminarraum 1, ground floor, 8102.EG.104) at Parkring 37 (entrance left of EDEKA) in Garching-Hochbrück.

Organization of classes:Stefan Junk
Groups:

Exercise classes will be held in two groups, each taking place every other week:

Group 1: Every second Wednesday, starting from October 14.

Group 2: Every second Wednesday, starting from October 21.

Please register to your favourite group in TUMonline starting October 13.

Corrections:Your exercise sheets will be corrected and graded with points. Please form groups of three and hand them in during the lecture or before the exercise class on the date indicated on the sheet.
Bonus system:

Through continuous participation you can add a bonus point to your final grade: At the end of the course, if you obtain 60% (or more) of the total points allotted to all the exercises, your grade will go one level up (if you got a 1.7, this will turn to 1.3, if you got 2.0, it will turn to 1.7 and so on). Improving the grade 1.0 or a failed (4.0 or worse) exam is not possible.

Course materials:The exercise sheets will be published on the Moodle page for this course. Once you register for one of the two groups, you will automatically be enrolled to the Moodle course and have access to the material.

If you have any questions concerning the exercise classes, please contact Stefan Junk.