# MA8704 Probability Theory and Asymptotic Methods (Fall 2019)

## Messages

- [03.12] The candidate list with examination times for December 6 is found here (revised 4 December). If you are a candidate and is not on the list, please send me an email. The exam will be in room 656.

- [19.11] You may visit me in my Office (11th floor SBII) for quest ions before the exam. Special Office hours: Tuesday 26.11 at 13:15-14; Wednesday 27.11 at 13:15-14. (Not in office on 28.11 and 29.11); Tuesday 03.12 at 13:15-14; Wednesday 04.12 at 13:15-14; Thursday 05.12 at 11:15-14. Or: You may send me an email to make an appointment.

- [19.11] The exam will be in room 656 on 6 December. A list with precise meeting time for each candidate will be posted before the exam. Note that the grading is "Pass/No pass" for both PhD and master students.

- [22.10] In the lecture hours on Monday November 18 will Lukas Anzeletti give a presentation on "Optimal transport" as part of exam in ST3201 Master seminar in Statistics.

- [17.09] Oral exam will be Friday December 6.

- [16.09] We will tomorrow (17.09) try to agree on a day for the oral exam to be held in late November or in December.

- [16.09] There are no lectures next week, i.e., September 23 and 24. A self-study program is found under "Lectures".

- [29.08] There are no lectures next week, i.e., September2 and 3. A self-study program is found under "Lectures".

- [23.08] I can now confirm that the lectures will be as expected from the Message below, i.e., Mondays 12:15-14 in room 656, SB2 (Simastuen); and Tuesdays 12:30 (NOTE!) - 14 in R59 Realfagbygget. First time: Monday 26 August.

- [20/08] Following the discussion in todays meeting the lectures will start next week and be Mondays 12:15-14 in room 656 SB2 (Simastuen) (or possibly 10:15-12, depending on a possible change of time in MA3402 - new information will be given before Monday), and Tuesdays 12:30-14 in R59 Realfagbygget (slightly depending also on MA3402 - new information will be given). Alternative time is Tuesday 16.15-18.

- [26/06] The first meeting will be Tuesday, August 20 in room 822, Sentralbygg 2, at 14:15. A brief introduction to the contents of the course will be given, while
*the main task is to find suitable times for lectures during the semester.*Due to other activities, I will need to have lectures on Monday, Tuesday, Wednesday. If you cannot come to this first meeting, you may send me an email if you have preferences for the lecture time.

- [25/06] Welcome to the home page of MA 8704 Probability Theory and Asymptotic Methods.

## Textbooks

**Main text:**

Alan F. Karr. Probability, 1993, Springer Verlag, (main text).

The book can be downloaded from NTNU freely from Springer Link

http://link.springer.com/book/10.1007%2F978-1-4612-0891-4

**Additional reading:**

Jean Jacod and Philip Protter. Probability Essentials. Second Edition. Springer-Verlag Berlin Heidelberg, 2004.

The book can be downloaded from NTNU freely from Springer Link:

https://link.springer.com/content/pdf/10.1007%2F978-3-642-55682-1.pdf

## Preliminary curriculum

- Chapter 1: 1.1-1.5
- Chapter 2: 2.1-2.6
- Chapter 3: 3.1-3.4
- Chapter 4: 4.1-4.5
- Chapter 5: 5.1-5.5
- Chapter 6: 6.1-6.6
- Chapter 7: 7.1-7.5
- Knowledge of main ideas of exercises studied in the lectures

## Lectures

Date | Textbook | Exercises | Comments, downloads etc. | Note | |
---|---|---|---|---|---|

26.08 | Probability | Chapter 1.1-1.2 | Proof of Theorem 1.17 Monotone Class Theorem. | ||

27.08 | Chapter 1.2-1.3.3 | Start at 10:30 | |||

02.09 | (Chapter 1.3.4-1.5) | Self-study. | No lecture (self study) | ||

03.09 | Random variables | (Chapter 2.1-2.2.3) | Self-study. | No lecture (self study) | |

09.09 | Chapter 1, Chapter 2.1-2.1.5 | 1.3,1.9,1.10, 1.18, 1.19 | Discussed the various topics from the self study | ||

10.09 | Chapter 2.1.6-2.6 | Finished chapter 2 | |||

16.09 | Independence | Chapter 3.1-3.4 | 2.1, 2.2, 2.3, 2.4, 2.5,2.11,2.12 | Discussed the main parts of Chapter 3, rest is for self-study next week. Discussed some exercises from Ch. 2, | |

17.09 | Expectation | Chapter 4.1 | From beginning of chapter 4 until Theorem 4.8. | ||

23.09 | (Chapter 3.1-3.4) | 3.5, 3.7, 3.9, 3.10, 3.13, 3.14 | Self-study 2. | No lecture (self study) | |

24.09 | (Chapter 3.1-3.4) | Self-study 2. | No lecture (self study) | ||

30.09 | Chapter 4.1 | We discussed briefly the self study 2 and went throug selected exercises from Chapter 3. . Then we continued on chapter 4 from Theorem 4.8 Fatou's lemma, which was discussed without proof, and finished Section 4.1. | |||

01.10 | Chapter 4.2 -4.3 | ||||

07.10 | Convergence of random variables | Chapter 4.4-4.5, 5.1 | 4.2, 4.14, 4.16, 4.19 | We first discussed sections 4.4 and 4.5 and the exercises for Ch. 4. Then we started to look at Chapter 5. | |

08.10 | Chapter 5.2 | We discussed the definitions and theorems, until 5.2.4. | |||

14.10 | Chapter 5.3-5.5 | Finished Chapter 5 | |||

15.10 | Characteristic functions | Chapter 6.1 | 5.1, 5.2, 5.5, 5.6, 5.7, 5.11, 5.15, 5.27 | Exercises for Chapter 5. Start on Chapter 6 | |

21.10 | Chapter 6.2 | ||||

22.10 | Chapter 6.3-6.4+6.6 | ||||

28.10 | Chapter 6.5 | 6.5, 6.7, 6.11, 6.12 | We completed Chapter 6.4 and 6.5 + discussed the exercises | ||

29.10 | Classical limit theorems | Chapter 7.1 | We started Chapter 7 (down page 186) | ||

04.11 | Chapter 7.2-7.3 | Continued on Chapter 7, until last few lines of proof of Theorem 7.11 (Lyapunov) | |||

05.11 | Chapter 7.3 | Worked on the proof of Theorem, 7.17 (Lindeberg). Last part of proof (p. 196) remains. | |||

11.11 | Chapter 7.3-7.5 | Prove Prop. 7.14. Exercises: , 7.2, 7.3, 7.9, 7.12, 7.25 | |||

12.11 | Chapter 7.3-7.5 | ||||

18.11 | "Optimal transport" (Lukas Anzeletti ) | Lukas Anzeletti gives a presentation on "Optimal transport" as part of exam in ST3201 | |||

19.11 | Overview | Chapters 1-7 | Final lecture |

## Lecturer

Professor Bo Lindqvist. Office: 1129, Sentralbygg 2. Email: bo [dot] lindqvist [at] ntnu [dot] no

## Schedule

- Mondays 12:15-14:00, Room 656, SB2 (Simastuen).
- Tuesdays 12:30-14:00, Room R59, Realfagbygget.

## Exam

Oral exam will be held on Friday December 6.