PROBABILITES AND EXPECTATIONS, 7.5 credit points

autumn 2010

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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 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 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 and Wendesdays, 10-12.

However, if that is not suitable, then we find other hours. The first session is on

Monday, 30 August, 10.00-11.45 in MVL15.

See you then!

Torgny Lindvall