PROBABILITES AND
EXPECTATIONS, 7.5 credit points autumn 2011
*****************************************************************
Teacher: Torgny Lindvall, office
MVH3015, phone connection: 3574, e-mail: lindvall@chalmers.se
*****************************************************************
The fundaments of
modern probability theory were laid in the first decades of the 20:th
century, following the development of measure and integration theory. In this
course, we will carefully study the connections between
- measures and probabilities,
- integrals and expectations, and
- product spaces and independence.
A crucial role here is played by Dynkin's lemma, using so
called pi-systems,
which are very convenient and effecient to use in probability theory.
The last main topic of the course is characteristic functions (=
Fourier transforms of probability measures) and their use to prove the central limit theorem.
Among other topics, we notice Kolmogorov's 0-1 law, and a probabilistic
proof
of Weierstrass' approximation theorem.
The book to be used is:
David Williams: Probability with Martingales, Cambridge University Press.
It is available in paperback.
If you are curious about the author,
you may click here : Williams.
And you may consult the excellent site
MacTutor
archive to learn about the
pioneers of measure and integration theory,
and probability theory: Borel, Lebesgue, Kolmogorov, Khinchin, Levy...
The preliminary schedule is that we
meet on Mondays and Wendesdays, 10-12.
However, if that is not suitable, then
we find other hours. The first session is on
Monday, 29 August, 10.00-11.45 in
MVL15.
See you then!
Torgny Lindvall