Measure theoretic probability 2009-2010
(ST406028)
Aim
To provide an introduction in the basic notions and results of measure theory and how these are used in probability theory.
Contents
During the course the measure theoretic foundations of probability theory will be treated. Key words for the course are: measurable space, limit theorems for Lebesgue integrals, product measures, random variables, distributions of random variables, different convergence concepts for random variables (convergence in probability, weak convergence, convergence in p-th mean) and relations between them, uniform integrability, conditional expectation and conditional distribution. All these topics will be present in the treatment of martingale theory in discrete time. Finally, the existence of Brownian motion is proved.
Prerequisites
Knowledge at the level of for instance Richard T. Durrett, The Essentials of Probability and the first seven chapters of Walter Rudin, Principles of Mathematical Analysis.
Literature
A new set of lecture notes (also containing the exercises) will be used as a substitute of literature used in the past.
People
Lectures by Bas Kleijn
Schedule
Fall semester, Wednesdays 10.15-13.00, location: Mauritskade 57, room 0.20. The course will start on September
9.
There will be no lecture on October 21.
Reimbursement of travel costs
Students who are registered in a master program in Mathematics at one of the Dutch universities can claim their travel expenses,
see the rules.
Exams
The retake of the written exam will take place on Monday 31 May 2010, 14:00-17:00, in room JK3.88 of the Van der Waals-Zeeman Institute, Valckenierstraat 65-67,
1018XE Amsterdam, see map 1 or map 2.
The written exam will be partly on theory and partly consist of ordinary exercises. You have to know some results and their proofs(!) by heart. At least one of them will return as a question in the exam. These results are
Lemma 1.13,
Theorem 4.11,
Theorem 6.7,
Theorem 7.15,
Theorem 10.10,
Proposition 11.7.
Links
Korteweg-de
Vries Institute for Mathematics
Master Stochastics and Financial Mathematics
Dutch Master Program in Mathematics .