# 107.A21 Selected chapters in Probability Theory This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2025S 2023S 2022S 2021S 2020S 2018S 2017S 2015S 2014S 2013S

2023S, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to explain the basic concepts and proof techniques in the theory of large deviations, and to understand its implications in a wide variety of applications.

## Subject of course

The theory of large deviations concerns the fast (exponential) decay of the probability of certain "rare" or "extreme" events. The most typical example of such rare events occurs when the sample mean of a sequence of independent and identically distributed random variables deviates from its mean, even when the sample size grows large.

In the first part of the course, we will analyse the most important results and concepts in large deviations theory:

• Cramér's theorem
• general large deviation principles
• Sanov's theorem
• Gärtner-Ellis theorem

In the second part of the course we will deal with (some of) the following applications of large deviations theory:

• statistics: asymptotic optimality of Bayesian decision tests
• information theory: compression algorithms
• statistical physics: ferromagnetic behaviour in the Curie-Weiss model
• financial risk theory: ruin probability of an insurance company

Lectures.

## Mode of examination

Oral

If less than 4 students show up, the course will be cancelled and reannounced next year.

Because of the Covid pandemic, it is possible that the teaching modality will be changed to "online".

## Course dates

DayTimeDateLocationDescription
Wed09:00 - 11:0001.03.2023 - 28.06.2023Seminarraum 107/1 Selected chapters in Probability Theory
Thu09:00 - 10:0002.03.2023 - 29.06.2023Seminarraum 107/1 Selected chapters in Probability Theory
Selected chapters in Probability Theory - Single appointments
DayDateTimeLocationDescription
Wed01.03.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu02.03.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed08.03.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu09.03.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed15.03.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu16.03.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed22.03.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu23.03.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed29.03.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu30.03.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed19.04.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu20.04.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed26.04.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu27.04.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed03.05.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu04.05.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed10.05.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Thu11.05.202309:00 - 10:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed17.05.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory
Wed24.05.202309:00 - 11:00Seminarraum 107/1 Selected chapters in Probability Theory

Oral exam

## Course registration

Begin End Deregistration end
20.02.2023 08:00

## Curricula

Study CodeObligationSemesterPrecon.Info
033 203 Statistics and Mathematics in Economics Mandatory elective
860 GW Optional Courses - Technical Mathematics Not specified

## Literature

Books:

• den Hollander - Large Deviations
• Dembo, Zeitouni - Large Deviations Techniques and Applications

## Previous knowledge

Measure and probability theory I-II (but any students who know the basics of probability theory will be able to follow).

English