Institute of Stochastics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.056 und 2.002

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

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

# Brownian Motion (Winter Semester 2012/13)

 Classes: Lecture (0105800), Problem class (0115800) 2+1

 Lecture: Problem class: Thursday 9:45-11:15 1C-04 Wednesday 15:45-17:15 Z 2

# Content

Brownian motion is one of the most important class of stochastic processes in continuous time and with continuous state space. It has applications in science, engineering and mathematical finance. The object of this course is to give a basic introduction into the theory of Brownian motion. This includes the intersection of Brownian motion with continuous Gaussian processes and continuous Markov processes, the construction and existence of Brownian motion and path properties.

# Problem classes

The problem classes will be given on a biweekly basis (with one exception in January). During these problem classes the exercises on a problem sheet will be discussed. The problem sheets will be issued in the lecture the week before the respective problem class and will also be available for download in the Studierendenportal.
Exemplary solutions to the problems will also be available for download. The password required to access the sheets and solutions will be announced in the lecture.
The students will not be able to turn their solutions to these sheets in for marking, however it is still encouraged to look into the problems before the respective problem class.
The problem class will take place on the following dates:

31. 10., 14. 11., 28. 11., 12. 12., 16. 01., 23. 01., 06. 02.

On Wednesday, the 9th of January there will be an additional lecture instead of a problem class. For this reason there will be no lecture on Thursday, the 17th of January.

# Prerequisites

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

# Examination

There will be oral exams at the end of the semester. They are currently planned to take place on Monday, the 25th of February 2013. It is now possible to sign up for the exams in the "Studierendenportal".

# References

• Durrett, R. (1984): Brownian motion and martingales in analysis. Wadsworth International Group, Belmont, CA.
• Karatzas, I. and Shreve, S. E. (1991): Brownian motion and stochastic calculus. 2nd Edition. Springer, New York.
• Klenke, A. (2008): Probability theory. Springer, London.
• Revuz, D. and Yor, M. (1999): Continuous martingales and Brownian motion. 3rd Edition. Springer, Berlin.
• Rogers, L. C. G. and Williams, D. (2000): Diffusions, Markov processes, and martingales. Volume 1. Cambridge University Press, Cambridge.
• Schilling, R. and Partzsch, L. (2012): Brownian Motion : An introduction to stochastic processes. De Gruyter, Berlin.