Program Overview

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Probability Theory Autumn 2024

Overview

The Probability Theory course is offered in Autumn 2024, with lectures taking place on Wednesdays and Fridays.

Lecturer and Coordinator

• Lecturer: Vincent Tassion
• Coordinator: Ritvik Radhakrishnan

Content

The course covers the following topics:

1. Fundamental results: law of large numbers, different notions of convergences for random variables, characteristic functions, convergence in law, central limit theorem.
2. Martingales: conditional expectation, almost sure convergence, optional stopping theorem.

Lectures

• There are two lectures per week:
  • Wednesday, 12:15 to 14:00 at ML H44
  • Friday, 10:15 to 12:00 at CAB G11

Lecture Notes

The course includes lecture notes on the following chapters:

1. Introduction and reminders
2. Chapter 1
3. Chapter 2
4. Chapter 3
5. Chapter 4
6. Chapter 5
7. Chapter 6
8. Chapter 7
9. Chapter 8
10. Chapter 9
11. Chapter 10
12. Chapter 11
13. Chapter 12
14. Chapter 13
15. Chapter 14
16. Chapter 15
17. Chapter 16

Exercises

• Students are encouraged to hand in written solutions to exercise sheets.
• Exercise sheets are due by the indicated Fridays at 18:00.
• Late submissions will not be considered.

Exercise Sheets

The following exercise sheets are assigned:

1. Exercise sheet 1 - due by 18:00, September 27
2. Exercise sheet 2 - due by 18:00, October 4
3. Exercise sheet 3 - due by 18:00, October 11
4. Exercise sheet 4 - due by 18:00, October 18
5. Exercise sheet 5 - due by 18:00, October 25
6. Exercise sheet 6 - due by 18:00, November 2
7. Exercise sheet 7 - due by 18:00, November 8
8. Exercise sheet 8 - due by 18:00, November 16
9. Exercise sheet 9 - due by 18:00, November 22
10. Exercise sheet 10 - due by 18:00, November 29
11. Exercise sheet 11 - due by 18:00, December 6
12. Exercise sheet 12 - due by 18:00, December 13
13. Exercise sheet 13 - due by 18:00, December 20

Exercise Classes

Exercise classes start from the second week of the semester and are held at the following times and locations:

1. Tuesday, 14:00-15:00, ML F 34, assistant: Ritvik Radhakrishnan
2. Tuesday, 14:00-15:00, ML H 41.1, assistant: Laury Verhoeven
3. Tuesday, 15:00-16:00, ML H 41.1, assistant: Nicolas Hotton

Exam Information

1. Information sheet
2. Past exams: Probability theory HS 23, Probability theory FS 24, WuS FS 24

Literature

The following texts are recommended:

1. J.F. Le Gall, Probability Theory, Springer 2022
2. D. Williams, Probability with martingales, Cambridge University Press 1991
3. R. Durrett, Probability: Theory and examples, Duxbury Press 1996
4. R.M. Dudley, Real Analysis and Probability, Cambridge University Press 2002