Mathematik-Gebäude, TU-Dortmund, Hörsaal E28

The generalized Ornstein-Uhlenbeck (GOU) process driven by a bivariate Lévy process is widely known for its applications e.g. in finance, insurance and physics. In this talk we present the generator of the GOU process and show that GOU processes are Feller processes. Using these results, we will then gather information on the stationary distributions of GOU processes, also known as exponential functionals of Lévy processes. In particular we can show that under some regularity conditions and for independent driving Lévy processes the mapping of (the law of) one Lévy process on the corresponding (law of the) exponential functional is injective and give conditions for continuity of this mapping in a distributional sense.
This is joint work with Alexander Lindner.

Dr. Anita Behme

TU München