| Week | Subjects |
|---|---|
| 1 | Review of Brownian motion and martingales. Reading: First two Chapters in Oksendal. |
| 2 | Stochastic integrals, Ito's formula Reading: Chapters 3 and 4. |
| 3 | Ito SDEs. Reading: Chapter 5. |
| 4 | Markov property, SDE and PDE. Reading: Notes. |
| 5 | Ito diffusions and PDE. Feynman-Kac formula. Stopping times and boundary value problems. Reading: Notes. |
| 6 | Ito diffusions and PDE. Feynman-Kac formula. Stopping times and boundary value problems. Reading: Notes. |
| 7 | The Girsanov transformation and applications to maximum likelihood estimation and importance sampling. Reading: Notes. |
| 8 | Introduction to Bayesian filtering. Reading: Notes. |
| 9 | More on filtering. |
| 10 | Introduction to stochastic control. Reading: Notes. |