Hinweis: Diese Veranstaltung wird im Wintersemester 2016/17 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 2016/17

Lecture

Dates:Wednesdays, 08:15 to 09:45 in room BC2 3.5.06 (Hochbrück-Seminarraum 3, 3rd floor) at Parkring 37 (entrance to the right of EDEKA) in Garching-Hochbrück.
Start: October 19, 2016
Instructor:Prof. Dr. Nina Gantert
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).

Exercises

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:There will be one exercise group, taking place every second week starting on October 19.
Corrections:Your exercise sheets will be corrected and graded with points. Please form groups of two or three, and hand in your solution  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 (4.3 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.