Graduate course on
Brownian motion and their intersection properties (4 points)
Meetings times: Wednesdays 15:15-17:00 and Fridays 13:15-15:00
in Room S4.
We begin this wednesday Feb 6th!
This course is actually the second part of a course on fractal geomety
if interested in what was covered in that class)
but this first half is NOT a prerequisite.
(If necessary, at some point, there will be two lectures quickly
giving the needed background on Hausdorff dimension and capacitarian
- If you are interested in the course but cannot come on Friday,
please email me your "busy times" as we will agree on a time
on that Friday.
- Also, if you want to attend the course or just keep informed about it,
please email me as I will be forming an email address list which
I will use to send future information.
The course will deal with the geometric aspects of
Brownian motion (the fundamental stochastic process) in Euclidean
space such as, which sets the Brownian motion can intersect,
the Hausdorff dimension of various related sets, the self-intersection
behavior of Brownian motion and (if time permits) relationships to
potential theory. A tentative outline of the topics which will be
Prerequisites: Integration theory and some elementary probability.
- Brownian motion
- Kakutani's criterion of which sets are hit by a Brownian motion
- Hausdorff dimension of Brownian motion paths in R^n
- Hausdorff dimension of the zero set of Brownian motion in R
- Self-intersection properties of Brownian motion paths
(where the critical dimension turns out to be 4)
- Solution of the Dirichlet problem using Brownian motion
- Relationship between packing dimension and Brownian motion paths
Kursexaminator: Jeff Steif (firstname.lastname@example.org)
Kursliterature: A collection of notes, class notes and
Last modified: Mon Feb 4 12:53:07 MET 2002