Brownian Motion and Stochastic Calculus

First lecture:
Tuesday, February 21.
First tutorial:
Tuesday, February 21.

Course attendence confirmation (Testat) requirements:
2/3 of all exercises reasonably tackled.

Tutorials:
Click here for information on the tutorials.

Question times ("Präsenz"):
Mondays and Thursdays, 12:00 – 13:00, in HG G 32.6.

Course content

This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed:

• Brownian motion: definition, construction, some important properties
• Markov processes: basics, strong Markov property, generators and martingale problems
• Stochastic calculus: semimartingales, stochastic integrals, Ito formula, Girsanov transformation, stochastic differential equations
• Levy processes: basic notions, some important properties

Prerequisites

Students are expected to have a solid knowledge of (measure-theoretic) probability theory as taught in the core course "Wahrscheinlichkeitstheorie". Lecture notes (in German) for the latter can be purchased during the "Präsenz".

Lecture notes

Lecture notes will be sold for CHF 15.- in the first lecture and later during the "Präsenz".

Performance assessment

• A numerical grade and ECTS points for the course are based only on the final 30 minutes oral examination. Exams will be in August 2012.
• A course attendence confirmation (Testat) is required to be admitted to the oral examination.
• In order to obtain the course attendence confirmation (Testat), students are required to make a reasonable attempt at solving at least 2/3 of all exercises.

References

• Durrett, R., "Stochastic Calculus. A Practical Introduction", CRC Press, 1996.
• Ikeda, N. and Watanabe, S., "Stochastic Differential Equations and Diffusion Processes", second edition, North Holland, Amsterdam, 1979.
• Karatzas, I. and Shreve, S., "Brownian Motion and Stochastic Calculus", second edition, Springer, Berlin, 1991.
• Revuz, D. and Yor, M., "Continuous Martingales and Brownian Motion", second edition, Springer, Berlin, 1994.
• Rogers, L.C.G. and Williams, D., "Diffusions, Markov Processes, and Martingales", vol. 1 and 2, Wiley, Chichester, 2000, 1994.
• Sato, K., "Levy Processes and Infinitely Divisible Distributions", Cambridge University Press, 1999.