Hinweis: Diese Veranstaltung wird im Wintersemester 2014/15 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 2014/15

Lecture:
Dates:Wednesdays, 08:15 to 09:45 in room 3.5.06 (Hochbrück-Seminarraum 3, 3rd floor, 8102.03.506) at Parkring 37 (entrance to the right of EDEKA) in Garching-Hochbrück.
Start: 8th October 2014
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 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).

Lecture Notes WiSe 2014/15

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. See dates. Note: First date ist 15th October 2014!

Organization of classes:Dr. Chiranjib Mukherjee
Bonus system:Your exercise sheets will be corrected and graded with points. 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.
Homework:
Sheet 1Sheet 2Sheet 3Sheet 4Sheet 5
Sheet 6Sheet 7Sheet 8  
Solutions:
Solution1 Solution1.2 MultinomSolution 2Solution 3Solution4Part1 Solution4Part2Solution 5
Solution 6Solution 7Solution 8 WeakConv 

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