Large deviations [MA5417]
Lecture
- Lecturer: Prof. Dr. Silke Rolles
- Time and location of the lecture: Wednesday, 8:15-9:45 in room 3.1.08 in Garching-Hochbrück, Parkring 35-39, 3rd floor (Seminarraum 1). If you walk up the stairs go straight through the glass door and enter the seminar room from the balcony.
- First lecture: Wednesday, October 17, 2012.
- Prerequisite: Probability theory (MA2409)
- Content: Large deviation theory is a part of probability theory that deals with the description of unlikely events and determines how fast their probabilities decay. This turns out to be crucial to study the integrals of exponential functionals of sums of random variables which come up in many different contents. The course will give an introduction to large deviation theory and its applications.
- Literature: The books will be on reserve in the library (Semesterapparat).
- Probability theory:
- R. Durrett: Probability: theory and examples, fourth edition, Cambridge University press, 2010.
- A. Klenke: Wahrscheinlichkeitstheorie, 2. Auflage, Springer, 2008. Link to the ebook of the first edition
- A. Klenke: Probability theory, Springer, 2008.
- Large deviations:
- A. Dembo and O. Zeitouni: Large deviations techniques and applications, second edition, Springer, 2010.
- F. den Hollander: Large deviations, American mathematical society, 2000.
- W. König: Große Abweichungen, Techniken und Anwendungen ^{}, Vorlesungsskript, 2006.
- F. Rassoul-Agha and T. Seppäläinen: A Course on Large Deviations with an Introduction to Gibbs Measures ^{}
- Probability theory:
- Syllabus
Final exams
- There will be a written final exam at the end of the course. Calculators, lecture notes, etc. are not allowed during the exam.
- The final exam will take place on February 27, 2013.
Homework and Tutorials
- Homework will be assigned every two weeks. You should try to solve all homework problems. You can work in groups of up to 3 students. Your solutions can be written in German or in English. Homework will be graded and returned during the tutorials. The solutions of the homework problems are discussed during the tutorials. Each exercise is graded from 0 to 4 points, where 4 stands for a perfect solution, 3 for few minor mistakes or missing arguments, 2 for major lacks and 1 for reasonably worked on. If an exercise consists of several parts, each of them has to be worked out reasonably for the whole exercise to count as reasonably worked out.
- Final grade: The final grade is the grade obtained in the final exam plus a possible bonus. If 70% of all homework problems are reasonably worked out, then you get a bonus: If you pass one of the final exams (i.e. your grade is 4.0 or better), then your grade is improved by 0.3 (for example 4.0 becomes 3.7, 3.7 becomes 3.3, 3.3 becomes 3.0 etc.). A grade of 1.0 is not changed.
- Time and location of the tutorial: every two weeks, Wednesday, 12-14, in room 0.01.04, Parkring 35-39, ground floor, Garching-Hochbrück (Seminarraum 1).
- The tutorials will take place on the following Wednesdays: October 24, November 7 and 21, December 5 and 19, January 16 and 30
- Homework problems: