Courses in Stochastics in Autumn 2007




Stefan Geiss

Probability Theory 2 and 3
MATS262, 3ov (5op) 26h
MATS263, 2ov (4op) 24h

Time and Place:
Wednesday     8-10 MaD 380
Thursday      8-10 MaD 381

First lecture: 12/09/2007

Description:  Doing computations for experiments one
often ends up with sums of independent random variables
and is interested in their limit distributions. Why do
we get sometimes a constant as limit and sometimes a
Gaussian random variable? Are there other possibilities?
But before: in what sense does the convergence take place?
To give an answer to part of these questions we use
Characteristic Functions, an important tool in probability.

Contents of the lecture:
 1. Modes of convergence of random variables
 2. Characteristic functions of random variables
 3. Limit distributions

Literature:
[1] H. Bauer: Probability Theory (de Gruyter)
[2] A.N. Shiryaev: Probability (Springer)

 Script (completed step by step)

Last demonstration: Tuesday, the 18th of December, 12-14, MAD 380.

Exercises:

Christel Geiss

Stokastiset mallit (Stochastic Modeling)
MATA271,  2ov (4op) 28h

Time and Place:
Monday    12-14 MaD 381
Tuesday   14-16 MaD 381

First lecture: 10/09/2007

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 arrive at the theory of Markov chains. We continue with simple applications of Markov chains in genetics and finally come to Markov Chain Monte Carlo methods.

Literature:
[1] P. Guttorp:  Stochastic Modeling of Scientific Data (Chapman & Hall)
[2] O. Häggström:  Finite Markov Chains and Algorithmic Applications
[3] Wai-Yuan Tan: Stochastic Models with Applications to Genetics, Cancers,
                  AIDS and Other Biomedical Systems

Script

Information:

Exercises:
  • 18/09/2007
  • 25/09/2007
  • 02/10/2007
  • 09/10/2007
  • 16/10/2007
  • 23/10/2007
  • 30/10/2007

    • Topics for the test


    Christel Geiss

    Vakuutusmatematiikkaa (Non-Life Insurance Mathematics)
    MATA275,  3 op (2 ov) 20h

    Time and Place:
    Monday    12-14 MaD 381
    Tuesday   14-16 MaD 381

    First lecture: 29/10/2007

    Description: Insurance against theft, car damage, fire - how
    to compute the amount one should pay for this? This question
    leads to the so called risk theory. Poisson processes and more
    general renewal processes will be introduced to model the risk
    and estimate the ruin probability.

    Literature:
    T. Mikosch: Non-Life Insurance Mathematics

    Exercises:
  • 06/11/2007
  • 13/11/2007
  • 20/11/2007
  • 27/11/2007
  • 04/12/2007
    • Topics for the test