`Courses in Stochastics in Spring 2003`

Christel Geiss

Stochastic Modeling
(Stokastiset mallit)

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

First lecture: 04/02/2003

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

Topics:
first mid-term examination
second mid-term examination

Stefan Geiss

Johdatus todennäköisyysteoriaan
(A quite short introduction into probability)
MAT283, 2 ov, 16 h

Time and Place: Tuesday 12-14 MaD 381
Thursday 8-10 MaD 381

First lecture: 07/01/2003

Description: Gaussian or other distributions and random variables are
the basic for stochastic modeling. For example, the error of a
measurement can be assumed to be Gaussian. But how to define
properly a Gaussian distribution or another distribution on
the real line R? And what are random variables?

Contents of the lecture:
-) Probability spaces
-) Some special distributions
-) Random variables
-) Beginning of integration

Literature:
A.N. Sirjaev: Probability (Springer)

Stefan Geiss

Todennäköisyysteoriaan
(Probability Theory)
MAT312, 34 h

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

First lecture: 03/02/2003

Description: Why do we get very often the Gaussian distribution as
a limit distribution as for example in the Central Limit Theorem
for quadratic integrable identically distributed independent random
variables? Are there limit theorems giving different distributions?
In what sense does the convergence take part? To give a very elegant
answer to part of these questions one can use %Fourier Analysis in
terms of 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)

Exercises:
Problems 10/02/2003
Problems 17/02/2003
Problems 24/02/2003
Problems 03/03/2003
Problems 17/03/2003
Problems 24/03/2003
Problems 07/04/2003
Problems 14/04/2003

CHANGE: The last demonstrations take part the 14-th of April and not the 7-th of April.

Self-study for the course Probability Theory
16 h (4 weeks, 2 ov)

Topic: Some limit theorems

Literature:
A. N. Shirjaev. Probability

Pages 309-341
-) III.1: Theorem 2
-) III.3 and III.4 with corresponding exercises
-) III.2: needed notation for III.3

Consultation times (MaD 340, 12:00-13:30): 14.04, 23.04, 28.04

Examination: Oral test