Martingales, Brownian Motion

1. Conditional expectation.

2. Martingales, stopping times, optional sampling.

3. Martingale convergence theorems, inequalities.

4. Elementary continuous-time stochastic processes: Poisson process, continuous-time Markov chains.

5. Brownian motion: definition, construction, basic properties.

Martingales associated to Brownian motion, brownion motion with drift.

6. Elementary introduction to the stochastic integral, Ito isometry

The final grade of the course consists of the following components:

- Two graded homeworks

- a written exam

A homework grade h is computed as the average of the scores on the two graded homeworks. Course grade is the final exam grade f or 0.6f+0.4h, whichever is larger, provided f>5.

Resit/ Repair opportunities:

In case of an insufficient result, repair opportunities may be offered in accordance with TER Implementation Regulations Art 5, sub 5., for:

- homework assignments and written exam: written resit

Disclaimer: information may change depending on unforeseen circumstances or measures (see: TER Art 29, sub 4).

The homework grade does not count for the resit.