PROBABILITES AND
EXPECTATIONS, 7.5 credit points
autumn 2009
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Teacher: Torgny Lindvall, office
MVH3015, phone connection: 3574, e-mail: lindvall@chalmers.se
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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 pisystems,
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 Weierstass' approximation theorem.
The book to be used is:
David Williams: Probability and
Expectations, 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 preiminary schedule is that we
meet on Mondays, 10-12, and
on Thursdays, 13-15.
However, if that is not suitable, then
we find other hours. The first session is on
Monday, 31 August, 10.00-11.45 in
MVL15.
See you then!
Torgny Lindvall