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