MATS254 Stochastic processes (4 cr)
Learning outcomes
After completion of the course, the student
* 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
Study methods
Course exam and exercises. Part of the exercises may be obligatory.
Final exam is an other option.
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)
Materials
Lecture notes: S. Geiss. Stochastic processes in discrete time
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| 978-0521406055 | D. Williams. Probability with martingales, 1991, Cambridge Mathematical Textbooks |
Assessment criteria
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.
Prerequisites
MATA280 Foundations of stochastics
Recommended: Measure theoretic foundation of probability
(MATS260 Probability 1 or MATS112 Measure and Integration Theory 2)