`Courses in Stochastics in Spring 2004`

Christel Geiss

Stochastic Modeling (Stokastiset mallit)
MAT 284, 3 ov

Time and Place:
Tiistaina 12-14 MaD 381
Torstaina 8-10 MaD 381

First lecture: 13/01/2004

Description: The financial market is as unpredictable as the weather!
Nevertheless,there are mathematical models to describe and understand
both of them better. Starting with random walk to model
stock prices and the weather, we come to the theory of Markov
chains. We continue with Markov Chain Monte Carlo methods as
an application.

Literature:
P. Guttorp : Stochastic Modeling of Scientific Data
O. Häggström: Finite Markov Chains and Algorithmic Applications

Exercises:
Problems 19/01/2004
Problems 26/01/2004
Problems 02/02/2004
Problems 09/02/2004
Problems 16/02/2004
Problems 23/02/2004
Problems 01/03/2004
Problems 08/03/2004
Problems 15/03/2004

Topics:
mid-term 18/02 + 25/02
2. mid-term 17/03 + 24/03

Stefan Geiss

Todennäköisyysteoria (Probability Theory)
MAT 312, 5 ov

Time and Place:
Monday 12-14 MaD 380
Tuesday 8-10 MaD 380

First lecture: 12/01/2004

Description: Doing computations for experiments, carried out several times,
one often ends up with sums of random variables and one is interested in
their limit distribution. Why do we get sometimes a constant as limit and
sometimes a Gaussian random variable? In what sense does the convergence
take part? To give an elegant answer to part of these questions one can
use Fourier Analysis via Characteristic Functions of random variables.

Contents of the lecture:
-) Modes of convergence of random variables
-) Characteristic functions
-) Some limit distributions

Literature:
H. Bauer: Probability Theory (de Gruyter)

Here You find a script for the lecture "Introduction to probability theory".
This script is still in a preliminary form. We would be happy about suggestions
and to get information about typing-misprints (and other mistakes).