Stochastiek

Credits	8 credit points
Instructors	Meester, R.W.J. (Vrije Universiteit)
E-mail	rwj.meester@few.vu.nl
Description	The material is chosen in such a way that the only background knowledge needed is elementary probability, yet the material is not part of any standard course in probability. We will mainly be concerned with random walks. In particular, we will explore the intimite relation between random walks and electrical networks. This leads to many results about random walks, for instance criteria whioch determine whether or not a random walk will return to its starting point for sure. A key ingredient is the concept of a harmonic function, and this gives a beautiful and useful connection between probability and analysis. Furthermore, we will use elementary but interesting counting methods to explore very surprising properties of random walks, for instance the famous arcsine law and the reflection principle. If time permits, we will also discuss a continuous version of a random walk – the so called Brownian motion.
Organization	Classes by teacher and by participants. Exercise classes as well.
Examination	Take home exam.
Literature	1) P. Doyle en J.L. Snell, Random walks and electric networks (1984), 2) R. Meester, A natural introduction to probability theory, 2^nd edition (2008). 3) probably more – this will be announced later.
Prerequisites	One introductory course in probability.

Last changed: 08-09-2010 09:56