This course is a rigorous introduction to the theory of Markov processes where emphasis is given to the certain aspects of Markov processes theory that often appear in applications to economics and finance.

Main topics include:
1. Markov property, transition functions and semigroups
2. Feller processes, regularity of paths, and right continuity of filtrations
3. Strong Markov property
4. Brownian motion
5. Martingale problem of Stroock and Varadhan
6. Connections to partial differential equations
7. Diffusions and stochastic differential equations
8. Equivalent measure changes for diffusion processes
9. h-transforms and Markov bridges
10. Linear and non-linear filtering with Markov signal and observation processes
11. Applications to financial markets with asymmetrically informed agents

Info zu Vorlesungzeiten

Bitte beachte/beachtenSie, dass die Vorlesung geblockt abgehalten wird.  Dr. Cetin wird einige Male nach Wien kommen und die Vorlesung dann zu den angegebenen Zeiten am Donnerstag und Freitag abhalten.  Unter "Einzeltermine" (direkt unter der Tabelle "LVA Termine") sieht man, welche Termine bereits fixiert sind.

Anmeldung nur für LVA-Unterlagen notwendig. / Registration only necessary for lecture notes.

1. R. M. Blumenthal and R. Getoor: Markov Processes and Potential Theory
2. K. L. Chung and J. Walsh: Markov Processes, Brownian Motion and Time Symmetry
3. I. Karatzas and S. Shreve: Brownian Motion and Stochastic Calculus
4. D. Revuz and M. Yor: Continuous Martingales and Brownian Motion
5. D. Stroock and S. Varadhan: Multidimensional diffusion processes

Knowledge of martingale theory and stochastic calculus at the level of Oksendal's Stochastic Differential Equations