# MATS254 Stochastic processes

### Course begins and ends

Oct 28, 2019 - Dec 22, 2019.### Course contents

##### Content

The course gives an introduction into the theory of martingales and some applications. Martingales are one of

the most important classes of stochastic processes. They are widely used in stochastic modelling and in pure mathematics itself. The content of the course is:

* martingales

* Doob's optional stopping theorem

* Doob's martingale convergence theorem

* applications (Branching Processes and Kakutani's Dichotomy Theorem)

##### Completion methods

Course exam and exercises. Part of the exercises may be obligatory.

Final exam is an other option.

##### Assessment details

The grade is based on

a) the number of points in the course exam and possibly additional points from exercises

OR

b) the number of points in the final exam.

At least half of the points are needed to pass the course.

* can calculate conditional expectations

* can decide whether a stochastic process is a martingale

* knows the basic conditions under which a martingale converges

* can apply martingales in stochastic modelling

### Literature

- D. Williams. Probability with martingales, 1991, Cambridge Mathematical Textbooks; ISBN: 978-0521406055