Measure theoretic probability
2002-2003

Contents

During the course the measure theoretic foundations of probability theory will be treated. Key words for the course are: 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, conditional expectation and conditional distribution. We also treat some martingale theory and Brownian motion.

Literature

D. Williams, Probability with martingales, Cambridge University Press (BUY IT!) and additional lecture notes.
Exercises are available as a ps and as a pdf file.

Examination

Homework exercises (please, write in english) and oral exam

Lecturer

P.J.C. Spreij

Schedule

Fall semester, Thursdays 13-16, room P.015B, the course will start on September 5
No classes on October 24 and on November 14

Participants


Programme

Week 1
 Class: Williams, chapters 1,2, sections 3.1-3.5, A1.2-A1.4
Homework: 4 exercises from `Week 1'
Week 2 Class: Williams, sections 3.8-3.12, 3.14, 4.1-4.4
Homework: 4 exercises from `Week 2'
Week 3 Class: Williams, sections 6.1 - 6.7 (together with the relevant companion material of chapter 5)
Homework: 4 exercises from `Week 3'
Week 4 Class: Williams, sections 6.10 - 6.13, 8.1 - 8.5
Homework: 4 exercises from `Week 4'
Week 5 Class: Williams, sections 9.1-9.8
Homework: 4 exercises from `Week 5'
Week 6 Class: Williams, sections 9.9, 9.10, 10.1-10.8 (martingale case only)
Homework: 4 exercises from `Week 6'
Week 7 Class: chapter 11, sectios 12.0-12.2, 12.6-12.7, 12.10
Homework: 4 exercises from `Week 7'
Week 8 Class: chapter 13, sections 14.1, 14.2
Homework: 4 exercises from `Week 8'
Week 9 Class: sections 14.3-14.6, 14.10-14.12, 14.17.
Homework: The exercises from `Week 9'
Week 10 Class: sections 17.1-17.4.
Homework: Three exercises from `Week 10'
Week 11 Class: section 17.5 of Williams, sections III.3-III.4 of Pollard.
Homework: 4 exercises from `Week 11'.
Week 12 Class: lecture notes (in ps or in pdf)
Homework: 4 exercises from `Week 12'.


To the Korteweg-de Vries Instituut voor Wiskunde or to the homepage of the master's programma.

Email: spreij@science.uva.nl