Advanced subjects of stochastic analysis as needed for continuous-time financial and actuarial mathematics.

Convergence of multidimensional normal distributions, multidimensional linear filtering theory, filter equations, zero-one laws (Blumenthal, Kolmogorov, Hewitt-Savage), introduction to Feller processes

oral Exam

• Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications. 6. Edition, Springer-Verlag, 2007, ISBN 978-3-54004-758-2.
• Daniel Revuz and Marc Yor: Continuous Martingales and Brownian Motion, 3. Edition, Springer-Verlag, 1999, ISBN 3-540-64325-7.
• Olav Kallenberg: Foundations of Modern Probability. 2. Edition, Springer-Verlag, 2002, ISBN 0-387-953113-2.