A new set of lecture notes (also containing the exercises) is in preparation. These will appear in parts and can be used as a substitute for the book by Williams.
If you mainly use the book, you follow the programme of the course in the first table below. If you use the new set of lecture notes, you find the programme in the second table.
The written exam will take place on 14 January 2009, 14:00 - 17:00, in room A.404, A-building of the Universiteit van Amsterdam, Roetersstraat 15, see travel directions. For those who can't participate, an alternative will be sought. More about this after January 14. The final grade will be an average of the results for the written exam and the homework assignments. Important minimum requirement for passing: 5.6 for the written exam. The material you have to study are book or lecture notes as far as treated in the lectures.
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. Part of the exam will be on this. These results are
(a) From Williams: Theorem 3.14, Theorem 6.13(a), Theorem 14.1, Lemma 17.4, Theorem 18.1 (only with Proof (a) under the assumption of tightness)
(b) From the Lecture Notes: Theorem 3.6, Theorem 4.33, Theorem 10.8, Proposition 11.7, Proposition 12.8
| 1 |
Class: Williams sections 1.2 - 1.6, 1.8 (partly), 1.9, 1.10, A1.2 - A1.4 ,2.1, 2.2, 2.6
Homework: From Chapter 1: 1, 2, 3, 6 (see ps and pdf files above) |
| 2 |
Class: Williams, Sections 2.3, 2.6 - 2.8, Chapter 3
Homework: Exercises from Chapter 3: 1, 3, 5 |
| 3 |
Class: Williams sections 4.1-4.3 and 5.1-5.7
Homework: Exercises from Chapter 4: 1 and 3, from Chapter 5: 1 and 5 (you may replace the construction of a decreasing sequence of simple functions buy constructing an increasing sequence below f and change the questions accordingly) |
| 4 |
Class: Williams sections 5.6 - 5.10, 5.12 - 5.14, 6.1 - 6.5, 6.12
Homework: Exercises from Chapter 5: 2, 3; from Chapter 6: 6 |
| 5 |
Class: Williams, L^p spaces, Holder and Minkowski inequalities, beginning of Chapter 8 on Fubini's theorem
Homework: From Chapter 6: 4, from Chapter 8: 4 assignement changed on Monday, October 13 |
| 6 |
Class: The remainder of Chapter 8.
Homework: From Chapter 8: exercises 1, 2, 5. Read also sections 1 and 2 from the Radon-Nikodym lecture notes. Theorem 2.1 will be used in class. |
| 7 |
Class: RN lecture notes, sections 3-5
Homework: Exercises (from the RN lecture notes) 7.2, 7.5 (it is meant that the X_k satisfy P(X_k=0)=P(X_k=1)=1/2), 7.7, 7.9 |
| 8 |
Class: Williams Sections 9.1 - 9.4, 9.7, 9.8
Homework: Read sections 9.6, 9.9, 9.10, make Exercises 2, 3, 4, 7 of Chapter 9 |
| 9 |
Class: Sections 10.1 - 10.10, Chapter 11
Homework: From Chapter 10: 2, 3, 5, from Chapter 11: 4 |
| 10 |
Class: Chapter 13, Sections 14.1, 14.2, 14.3, 14.4, 14.5, 17.1
Homework: Chapter 13, Exercises 2 and 4a; Chapter 14, Exercises 4, 7 |
| 11 |
Class: Sections 17.2 - 17.5, Chapter 16
Homework: Chapter 17, Exercises 1, 3, 8 and compute the characteristic function φ of the N(0,1) distribution. Hint: show first that φ'(u)=-uφ(u). What is the characteristic function of the N(μ,σ2) distribution? |
| 12 |
Class: Section 18.1, 18.3, 18.4 and Section 3 from a set of lecture notes.
Homework: Exercises 4.4, 4.8, 4.9 from the lecture notes; deadline 14 January 2009. |
| 1 |
Class: Lecture notes, Chapter 1
Homework: exercises 1.1, 1.3, 1.6, 1.9 |
| 2 |
Class: Lecture notes, Sections 3.1 and 3.2
Homework: Exercises 3.1, 3.3, 3.5 |
| 3 |
Class: Sections 3.3, 4.1 and 4.2 up to Definition 4.16
Homework: Exercises 3.8, 3.9, 4.2, 4.3, 4.6 |
| 4 |
Class: Sections 4.2 from Definition 4.16, 4.3, 4.4 up to Example 4.25
Homework: Exercises 4.5, 4.8, 4.9, 4.11 |
| 5 |
Class: L^p spaces, Holder and Minkowski inequalities, start with Chapter 5.
Homework: 4.10 (optional exercise, assignment changed on Monday October 13), 4.12, 5.8 |
| 6 |
Class: Remainder of Chapter 5
Homework: Exercises 5.2, 5.6, 4.7, 5.9. Read also sections 6.1 and 6.2. Theorem 6.1 will be used during class |
| 7 |
Class: Most of sections 6.3, 6.4, 6.5
Homework: Exercises 6.2, 6.5 (it is meant that the X_k satisfy P(X_k=0)=P(X_k=1)=1/2), 6.7, 6.9 |
| 8 |
Class: Section 8.1
Homework: Read section 8.2 (skip the proofs if you want), make Exercises 8.2, 8.4, 8.5, 8.6 |
| 9 |
Class: Sections 9.1, 9.2, 10.1
Homework: Exercises 9.3, 9.5, 9.6, 10.5 |
| 10 |
Class: Sections 7.2, 10.2, 10.4, 11.1 up to Proposition 11.2
Homework: Exercises 7.9, 7.10(a), 10.8, 10.10 |
| 11 |
Class: Sections 11.1, 12.1
Homework: Exercises 11.1 (only that convergence in probability implies weak convergence), 11.4, 11.9, 12.3(a,b) |
| 12 |
Class: Sections 12.2, 12.3. NB: the proof of Theorem 12.10 was a mess and also Lemma 12.12 suffered from some inaccuracies. In the version of the lecture notes of December 12 the errors have been corrected.
Homework: Exercises 11.11, 12.2, 12.8; deadline 14 January 2009. |