Courses in Stochastics in Spring 2008
Stefan Geiss
Stokastiset prosessit 1 ja 2
(Stochastic processes 1 and 2)
MATS252, 5 op (3ov), 26 h
MATS253, 4 op (2ov), 24 h
Time and Place
| Monday |
: |
12-14 MaD 380 |
| Tuesday |
: |
08-10 MaD 380 |
| First lecture |
: |
14/01/2008 |
Description: Assume that you have a fair coin and play the following
game: You and a second player have a starting capital of about 100 Euro. The
coin will be flipped and if you have tails, then you get 1 Euro from the
other player, in the other case you have to give her or him 1 Euro. One may
ask the following questions:
- What can be said about the length of the game, assuming that the game
ends if one of the players has lost all the money
- What is the probability that the game never ends?
- What is the probability that you loose all your money before your
partner looses all her or his money?
The course will answer these questions. For example, the first question is
related to the beautiful and surprising Law of Iterated Logarithm.
Contents of the course
- Sums of independent random variables
- Martingale theory
Literature
- D. Williams:
Probability with Martingales (Cambridge)
- A.N. Sirjaev:
Probability (Springer)
-
Script
Exercises
Christel Geiss
Todennäköisyysteoria 1
(Probability Theory 1)
MATA261, 5 op (3ov), 32 h
Time and Place
| Tuesday |
: |
12-14 MaD 381 |
| Thursday |
: |
12-14 MaD 381 |
| First lecture |
: |
15/01/2008 |
Description:
To describe and understand random phenomena by mathematical means one uses
probability theory. In the course we will introduce probability measures and
study their properties. Then we will deal with random variables, relate
independence to product spaces, and consider the expected value
of a random variable. Finally, we will realise what is special about
the Gaussian distribution that it can be used to model, for example,
measuring errors.
Probability Theory
1 is the basic course of the Stochastic Line, its
content is needed in all other stochastic courses.
Literature
- A. Gut:
Probability: a graduate course (Springer)
-
Script
Exercises