MATS352 Stochastic Analysis (5 cr)

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Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020

Description

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
* Itô's formula as an extension of the Taylor formula from calculus

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.

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 Itô's formula in various situations.

Description of prerequisites

Course MATS262 Probability 2 or similar.
Recommended: MATS254 Stochastic processes or similar.

Study materials

Lecture notes: S. Geiss. Stochastic differential equations (chapters 1-3)

Literature

  • Karatzas, Ioannis, Shreve, Steven: Brownian Motion and Stochastic Calculus, 1998, Springer; ISBN: 978-1-4612-0949-2

Completion methods

Method 1

Select all marked parts

Method 2

Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English

Teaching