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 semigroups2. Feller processes, regularity of paths, and right continuity of filtrations3. Strong Markov property4. Brownian motion5. Martingale problem of Stroock and Varadhan6. Connections to partial differential equations7. Diffusions and stochastic differential equations8. Equivalent measure changes for diffusion processes9. h-transforms and Markov bridges10. Linear and non-linear filtering with Markov signal and observation processes11. Applications to financial markets with asymmetrically informed agents
Anmeldung nur für LVA-Unterlagen notwendig. / Registration only necessary for lecture notes.
1. R. M. Blumenthal and R. Getoor: Markov Processes and Potential Theory2. K. L. Chung and J. Walsh: Markov Processes, Brownian Motion and Time Symmetry3. I. Karatzas and S. Shreve: Brownian Motion and Stochastic Calculus4. D. Revuz and M. Yor: Continuous Martingales and Brownian Motion5. D. Stroock and S. Varadhan: Multidimensional diffusion processes
Knowledge of martingale theory and stochastic calculus at the level of Oksendal's Stochastic Differential Equations