MSF500/MVE410: Weak Convergence (7.5 points)

The course takes place in March-May 2017.
It is intended for PhD students and last year Master students. After having taken the course, one should be able to 

- explain the details of the proofs of the main theorems covered in the course, especially the Functional Central Limit Theorem,
- solve the exercises given in the compendium, 
- demonstrate understanding of the key concepts and ideas concerning the weak convergence of probability measures, such as tightness and Skorokhod convergence.

Lecturer and examiner: Serik Sagitov

Key words: Functional central limit theorem, weak convergence in C[0,1], Skorokhod topology, tightness in D[0,1].
Prerequisite courses: Integration theory, Foundations of probability.
Literature: Convergence of probability measures, 2nd ed. by Billingsley.
Lecture notes: can be downloaded from here. Course digest: by O. Elias can be downloaded from here.
 (You might also find useful my extended lecture notes for another course: Stochastic processes.)

Timetable: 7 lectures on Tuesdays 10.00-11.45 at MVH11. Schedule for coverage of the Lecture Notes:

  1. March 21, Introduction, Chapter 1
  2. March 28, Chapters 2, 3
  3. April 4, Chapter 4
  4. April 25, Chapter 5
  5. May 2, Chapters 6, 7.1, 7.2
  6. May 9, Chapters 7.3, 7.4, 8
  7. May 16, Chapter 9 (13.15 at MVH12)


Examination. Instructions for the examination (a date to be fixed between you and me)

Lists of students

List-2017, List-2015, List-2013

Previous courses

2013 course page

2010 course page by Sergei Zuev

2002 course by Patrik Albin