Welcome to the Martingale Theory course. The Theory of Martingales is an extremely useful tool in Stochastic Processes, Financial Mathematics, Branching Theory, Diffusion Theory and Partial differential Equations.

This course is a must for any PhD student studying Probability and Statistics (yes, it's obligatory for a reason). It will be interesting for any Master student wanting to know more about the rigorous Probability theory. Anybody doing Financial Mathematics also has to learn Martingales sooner or later, to deal with Black-Scholes theory.

The schedule for the course can be found via the link to webTimeEdit top of the page.

D. Williams: Probability with martingales, Cambridge Mathematical Textbooks Cambridge University Press, Cambridge, 1991. ISBN: 0-521-40455-X;0-521-40605-6

We will cover Conditional Expectations, Martingales, Doobs Optimal Stopping Theorem, Convergence of Martingales, L^2-bounded Martingales, Kolmogorov's Strong Law of Large Numbers and Uniform Integrability. If we have time after that, we will also go through some interesting applications. The detailed syllabus is to appear soon.

Basic knowledge of probability and measure theory. Preferrably, one of the two courses "Probabilities and Expectations" or "Measure and Integration theory".

There is two homeworks:

first,

second. The deadline is March 5th, 16:00, which is one week before the examination time.

The written exam is March 12, 10:00-15:00 in MVH:12

The examination will consist of 3 theoretical questions and 2-3
problems similar to those you had in your homeworks.
In the theoretical part you will be asked to formulate and prove some
of the results we proved in the course. You will be able to use one A4
sheet of your own handwritten notes on which you can write any theorems, lemmas, proofs, whatever you wish. The list of topics is available

here.
In the practical part you will be asked to prove some kind of a
statement and/or give (counter)example for some statement. A lot like
the homeworks.
The total mark for the course will consist of the written exam in the end of the course (75%) and two home assignments, 12.5% each.