(7 1/2 points)
Spring 2018, 3rd reading period
Lecturer and examinator: Jeffrey Steif
Class times and place
To be determined.
to be put up.
The aim of the course is that the students learn some of the standard
material usually covered in a Ph.D.
course in probability theory.
These include, among other things,
weak law of large numbers, strong law
of large numbers, random series,
characteristic functions (aka Fourier transforms), the central limit
theorem and Brownian motion.
This course is intended for graduate students in
mathematics, mathematical statistics
as well as masters students with appropriate backgrounds.
(Please feel free to discuss your backround with me to see
if it is suitable).
Faculty are also of course very welcome.
PRELIMINARY TOPICS TO BE COVERED:
Setting up the language of probability theory in terms of
measure and integration theory.
Quick review of a.s. convergence, convergence in probability, convergence
in L_p and convergence in distribution (aka weak* convergence).
General Weak Law of Large Numbers including triangular arrays with
General Strong Law of Large Numbers.
Convergence in distribution, characteristic functions (aka
Fourier transforms) and the Central Limit Theorem.
The Lindeberg-Feller Theorem and some applications.
Introduction to Brownian motion and some of its elementary sample
Integration theory and having seen
some elementary probability theory (feel free to come
discuss your background with me).
There will not be one specific book that
the course will be based on and all of the following
(for which you can find PDF files for on the internet)
are very good books.
Perhaps the book that will be closest
to the lectures is Durrett's.
Probability: Theory and Examples by Richard Durrett
A first course in probability theory by Kai Lai Chung
Probability and Measure by Patrick Billingsley
There will be some homeworks and a final oral exam.
For masters students, the final might (or might not) be a written exam.
Jeff Steif (email@example.com)
Please email Jeff Steif (firstname.lastname@example.org) for registration.
(If you are already on the email list, you do not need to do this.)
Last modified: Tuesday November 28 1 10:15:34 MET DST 2017