MATS352 Stochastic Analysis (5 cr)
Learning outcomes
The students understand basic properties of the Brownian motion and can verify some of them. They are familiar with the construction of stochastic integrals. The students are able to compute particular stochastic integrals and to apply It么's formula in various situations.
Study methods
Course exam and exercises. Part of the exercises may be obligatory.
Final exam is an other option.
Content
The course introduces basics of stochastic analysis. One cornerstone is the Brownian motion, probably one of the most important stochastic processes. The course will cover:
* definition of the Brownian motion, its construction, and basic properties
* Stochastic integrals as an extension of Riemann-integrals
* It么's formula as an extension of the Taylor formula from calculus
Materials
Lecture notes: S. Geiss. Stochastic differential equations (chapters 1-3)
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| 978-1-4612-0949-2 | Karatzas, Ioannis, Shreve, Steven: Brownian Motion and Stochastic Calculus, 1998, Springer |
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
Course MATS262 Probability 2 or similar.
Recommended: MATS254 Stochastic processes or similar.