TKK / Institute of Mathematics / teaching /

Mat-1.3602 Stokastinen analyysi/Stochastic Analysis, spring 2008 (5 new credits)

The purpose is to give introduction to discrete time martingale theory and stochastic calculus with respect to continuous martingales, in particular with respect to standard Brownian motion.

Prerequisites (recommended):
Mat-1.3601 Johdatus stokastiikkaan/Introduction to Stochastics
Mat-2.3111 Stokastiset prosessit/Stochastic Processes

Contents:
1. Conditional expectation
2. Discrete time martingales
3. Brownian motion and continuous martingales
4. Stochastic integrals
5. Applications, part I: Girsanov theorem, Levy theorem, iterated integrals
6. Stochastic differential equations
7. Applications, part II [if the time permits]

Lectures:

Professor Esko Valkeila

Th 9 - 12 U261 Tu 9 - 12 Y405
First lecture Th 13.03. 2008 and last lecture Tu 29.04. 2008
Language: Finnish [English on demand]

Lecture note 1

Exams: May 16, 13 - 16

Exercises:

Assistant Ehsan Azmoodeh

Language: English
Exercise class Th 14-16 U356
Exeptionally first exercise class Tu 18.03. 2008, 14-16 U356 and last exercise class Tu 29.04. 14-16 U356

Exercise sheet 1

Course material:

Typeset handouts based on the following references:

• K.L. Chung, R.J. Williams: Introduction to Stochastic Integration, Birkhäuser
• J. Jacod, P. Protter: Probability Essentials, Springer
• Karatzas, S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer
• D. Revuz, M. Yor: Continuous Martingales and Brownian Motion, Springer
• A.D. Ventsel: A Course in the Theory of Random Processes (in Russian), Nauka