Universität Duisburg-Essen
Fakultät für Mathematik, Campus Essen
Arbeitsgruppe Wahrscheinlichkeitstheorie

Wolfgang Löhr

Lecture (3+1SWS), Winter 2016/17, "Vertiefungsmodul" for master students

Large Deviations (Große Abweichungen)

Time and Room: Tuesday 10:15h - 12:00h in WSC-S-U-3.02 (new room WSC-S-3.14) and Thursday, 10:15h - 12:00h in WSC-S-U-3.01

No class from 21st of November until 3rd of December!

ECTS credits: 6
If you need 9 ECTS credits, it is possible to give a presentation at the end of the semester.

The course is directed to master students (Vertiefungsmodul Stochastik). It integrates lectures and exercise classes of 4SWS in total, roughly split as 3SWS of lecture and 1SWS of exercises. The course has a final exam (written or oral depending on number of participants). The instruction language is English, unless all participants prefer German.

Content of the Lecture: Large deviation theory deals with "rare events" (with exponentially low probability, such as geting head more than 60% of the time when throwing a fair coin very often) and the quantification of how rare they are in terms of an exponential decay rate. Thus one obtains the speed of convergence for laws of large numbers. We develop an abstract theory in analogy to the theory of weak convergence on Polish spaces. Large deviation theory has many applications in information theory, ergodic theory, statistics, statistical mechanics, financial mathematics and other fields.


Exercise sheets:

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Last updated: 2016/11/17