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
|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|
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.
Amir Dembo, Ofer Zeitouni: Large Deviations Techniques and Applications,
Frank den Hollander: Large Deviations,
|Dates of classes:|
|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.|
|Solution1 Solution1.2 Multinom||Solution 2||Solution 3||Solution4Part1 Solution4Part2||Solution 5|
|Solution 6||Solution 7||Solution 8||WeakConv|
If you have any questions concerning the exercise classes, please contact Dr. Chiranjib Mukherjee.