Hinweis: Diese Veranstaltung wird im Wintersemester 2018/19 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 2018/19

Lecture

Dates: Thursdays, 14:15 to 15:45 in room BC1 2.02.01 (Hochbrück-Seminarraum, 3rd floor) at Parkring 11 in Garching-Hochbrück.
First Class: October 18
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 optimal 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).

Final Exam

There will be oral exams at the end of the semester.

Exercises

Dates of classes:

Wednesdays, 12:15 to 13:45 in room BC2 3.5.06 (Hochbrück-Seminarraum 3, 3rd floor) at Parkring 37 (entrance to the right of EDEKA) in Garching-Hochbrück.

The exercises will take place every second week, starting on October 31. Please check TUMonline for the precise schedule.

Organization of classes: Thomas Höfelsauer
 
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 E-Tests in Moodle, 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 (4.3 or worse) exam is not possible.
Course material: The exercise sheets will be published on the Moodle page for this course. Once you register for the exercise classes, you will automatically be enrolled to the Moodle course and have access to the material.