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Institute of Stochastics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.056 und 2.002

Address
Hausadresse:
Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Englerstr. 2
D-76131 Karlsruhe

Postadresse:
Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Postfach 6980
D-76049 Karlsruhe

Office hours:
Mo-Fr 10:00 - 12:00

Tel.: +49 721 608 43270/43265

Fax.: +49 721 608 46066

Levy Processes (Summer Semester 2013)

Classes: Lecture (0161300)
Weekly hours: 2


Note:

The class on 10.07.2013 will be moved to Friday 24.05.2013, 8:00-9:30, 1C-04.
Schedule
Lecture: Wednesday 8:00-9:30 1C-02

Content

Lévy processes as continuous-time analogue of random walks are one of the most basic and fundamental classes of stochastic processes including Brownian motion and Poisson processes. They have many applications in stochastic modeling as for instance in insurance, finance, queuing theory and telecommunication. This course gives a basic introduction into the theory of Lévy processes. The aim of this course is to have a basic knowledge of Lévy processes and infinitely divisible distributions. This includes the famous Lévy-Ito decomposition and path properties. In particular, subordinators and stable Lévy processes will be investigated in detail.

Prerequisites

Knowledge of probability theory as it is treated in the standard course "Wahrscheinlichkeitstheorie".

Examination

On the following dates it is possible to take an oral exam about the lecture:

  • Wednesday, the 31st of July 2013
  • Friday, the 6th of September 2013
  • Wednesday, the 9th of October 2013

If you wish to take an exam, please sign up by entering your name in the lists kept by the secretary of the Institut, Mrs. Tatjana Dominic (Room 5A-22 in the Allianz building). Master students are also required to sign up online through the QISPOS system, this is already possible. Diploma students wishing to take a study-accompanying exam ("studienbegleitende Prüfung") are required to bring their permit along to the exam.

References

  • Applebaum, D. (2004) Lévy Processes and Stochastic Calculus. Cambridge University Press, Cambridge.
  • Bertoin, J. (1996) Lévy Processes. Cambridge University Press.
  • Kyprianou, A. E. (2006) Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer.
  • Sato, K. (1999) Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge.
  • Schoutens, W. (2003) Lévy Processes in Finance. John Wiley & Sons.