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