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401-4934-08L 4 Credits DR , MSC D-USYS , D-MTEC , D-BAUG , D-MAVT , D-INFK , D-MATH , D-BIOL , D-ERDW , D-GESS , D-ITET , D-CHAB

The Theory of Extremes and Point Processes

Lecturers & Examiners: Prof. em. Dr. Paul Embrechts
VVZ CR n/a

Last Updated: 2026-02-05 15:29:50

Abstract

The aim of this course is to give a mathematical introduction to the modelling of extremes. Topics treated include: one-dimensional EVT, maximal domain of attraction, Peaks Over Threshold, regular variation (one-dimensional as well as more dimensional), multivariate extremes (componentwise approach), point processes methodology.

Objective

The aim of this course is to give a mathematical introduction to the modelling of extremes. As a basic methodological tool, the theory of point processes will be presented. Topics treated include: one- dimensional EVT, maximal domain of attraction (The Fisher-Tippett Theorem), Peaks Over Threshold (The Pickands-Balkema-de Haan Theorem), regular variation (one-dimensional as well as more dimensional), multivariate extremes (MEVT, componentwise approach), point processes methodology. The main trust of the course will be the mathematical modelling of extremes, however, throughout some applications of the theory will be discussed.

Content

This course mainly treats the probabilistic theory of extremes and point processes. It consists of the following larger blocks: 1. One-dimensional Extreme Value Theory (EVT). 2. The Theory of Point Processes and Applications to EVT. 3. An Introduction to the Theory of Multivariate Extremes.

Resources

Lecture Notes

This course will mainly be based on the following text:Sidney I. Resnick (1987) Extreme Values, Regular Variation, and Point Processes. Springer, New York.As this text is out of print, whenever necessary, some handouts will be given to the students.

Literature

Sidney I. Resnick (1987) Extreme Values, Regular Variation, and Point Processes. Springer, New York. Paul Embrechts, Claudia Klueppelberg and Thomas Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer, Berlin. Laurens de Haan and Ana Ferreira (2006) Extreme Value Theory. An Introduction. Springer, Berlin. Sidney I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. Springer, NY.

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
oral 20 minutes

Course Components

Type Title Time & Place Hours
lecture The Theory of Extremes and Point Processes
  • Thu 10:15-12:00 (HG D 1.2)
2 h weekly

Offered In