Courses in Stochastics in Spring 2002

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

      First lecture      :  22/01/2002

     Description:  The financial market is as unpredictable as the weather! Nevertheless,
     one can find mathematical models to describe and understand both of them.
     Starting with easy stochastic processes like random walk to model
     stock prices or  precipitation, we come to the theory of Markov chains. We
     continue with  Markov Chain Monte Carlo methods as a naturaland useful application
     to Markov chains and shall see at the end of the course how these MCMC-methods
     work, using the Statistics package BUGS, at the computer.

     Exercises
     Problems 29/01/2002 (English)
     Problems 29/01/2002 (suomeksi)
     Problems 04/02/2002 (English)
     Problems 04/02/2002 (suomeksi)
     Problems 11/02/2002 (English)
     Problems 11/02/2002 (suomeksi)
     Problems 18/02/2002 (English)
     Problems 18/02/2002 (suomeksi)
     Problems 25/02/2002 (English)
     Problems 25/02/2002 (suomeksi)
     Problems 04/03/2002 (English)
     Problems 04/03/2002 (suomeksi)
     Problems 11/03/2002 (English)
     Problems 11/03/2002 (suomeksi)
     Problems 18/03/2002 (English)
     Problems 18/03/2002 (suomeksi)
     Problems 08/04/2002 (English)
     Problems 08/04/2002 (suomeksi)

     Topics for final examination

 2) Stefan Geiss
     Stochastic Partial Differential Equations
     (Stokastiset Osittaisdifferentiaaliyhtälöt)

     Time and Place :   Monday  12-14 MaD 380
                                    Tuesday    8-10 MaD 380
     First lecture       : 14/01/2002

     Description:  Many phenomena are modeled by partial differential
     equations. For example the vibrating string can be modeled by the
     wave equation. But what happens, if the vibrating string is influenced
     by random perturbations?  'Think for example of a guitar carelessly left
     outdoors' [1]. What is the right model for such a situation? This question
     leads straight to Stochastic Partial Differential Equations. The lecture
     gives an introduction to these Stochastic Partial Differential Equations.
     We mainly concentrate on the one-dimensional case  (for example the
     vibrating string and not the drumhead), where  the methods are self-
     contained and elementary. The contents is planed as follows:

     0.  Introduction: A guitar left outdoors or a 'randomized' wave equation
     1.  Stochastic processes
          - Basic definitions
          - Brownian motion
     2.  The white noise and the Brownian sheet
          - Basic definitions
          - Sample function properties
     3.  Stochastic integrals
     4.  Stochastic Partial Differential Equations in one dimension
          -Wave equation
          - An example from Neurophysiology
          - Linear equation
          - Barrier problem
     5.  Remarks to  Stochastic Partial Differential Equations in
          higher dimensions

     Literature:

     [1]  J.B. Walsh: An introduction to partial differential equations

     Exercises
     Problems 22/01/2002
     Problems 29/01/2002
     Problems 05/02/2002
     Problems 12/02/2002
     Problems 05/03/2002
     Problems 12/03/2002
     Problems 19/03/2002
     Problems 26/03/2002
     Problems 09/04/2002
     Problems 16/03/2002
     Problems 23/04/2002