After successful completion of the course, students are able to show excellence in special fields of probability.
After having successfully completed the course, students are able to work with random point processes, Levy processes and to apply them in various fields of mathematics.
A large part of these lectures will be devoted to Levy processes, that are continuous-time stochastic processes with independent and stationary increments, and play an important role in applications (e.g. financial and actuarial mathematics). Levy processes include the famous cases of the Poisson process and the Brownian motion, but also the so-called stable processes and subordinators. We will develop the theory of Levy processes starting from the basics. Some preliminary lectures will be devoted to random point processes and in particular to Poisson point processes, that play an important role in the construction of Levy processes.
Lectures will take place in English. They will take place in person (with no streaming or recording); only in case of new lockdown they will be online.
I will use parts of the following books
- A. Kyprianou, Introductory lectures on fluctuations of Levy processes with applications
- J. Bertoin, Levy processes
Office hours for students: Tuesdays 2 p.m. - 3 p.m.
oral exam
Measure & Probability Theory. Preferably also some knowledge of Stochastic processes
