MA8109 Stochastic processes and differential equations
Fall 2023
Welcome to MA8109 !
This PhD course is given every second year, and usually 4th and 5th year (Master) students take it along with PhD students.
What is this course about?
- The course is about stochastic processes and differential equations with noisy/uncertain coefficients, so-called stochastic differential equations (SDEs): mathematical/probabilistic background, stochastic processes, Ito integral, Ito calculus, SDEs, diffusions, and some applications. Of the multitude of applications in science, engineering and other disciplines, we mention diffusions in Physics (Einstein, Ornstein-Uhlenbeck, Langevin) and option pricing in finance (Black-Scholes).
See 'General Information' in the menu for more info.
Who can take this course?
- Interested students at Master or PhD level.
- The level should be suitable for good 4th year students in the industrial mathematics program.
- It can be taken as a regular course (MA8109) or a 'fordypningsemne' (TMA4505).
Messages
| Date | Title | Message |
|---|---|---|
| 18.12. | Exams jan 2024 | Thursday January 4, room 1148 SB2: 10:15-11:00 Johanna 11:05-11:50 Peng Thursday January 11, room 1148 SB2: 15:00-15:45 Jacob |
| 01.12. | Office hour today | There will be an online meeting for Johanne and Ulrik today (14:45-15:30), they have got a zoom invitation by email. |
| 15.11. | Exam | 45 min oral exam. Check schedule below: Monday December 4, room 656 SB2: 10:15-11:00 Johanne 11:05-11:50 Ulrik (TMA4505) Friday December 15, room 656 SB2: 09:00-09:45 Jacob 09:50-10:35 Johanna 10:40-11:25 Robin 11:30-12:15 Peng 13:00-13:45 Sindre (TMA4505) 13:50-14:35 Maximillian 14:40-15:25 Torjei |
| Project | Deadline December 1: Email me the written report. More info under 'The Project' in the menu. \\ |
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| Q&A session | Wednesday 22.11. 9:15-10:00 in F4, gamle fysikk. You can ask questions about the course, curriculum, exam etc. |
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| Curriculum | The final curriculum is now fixed, see 'General information' in the menu. |
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| Notes of Espen | The notes from every lecture are now available, see 'General info' in the menu. |
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| Exercises | All solutions now published, see 'Homework' in the menu. |
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| Reference group | Final meeting 22.11.2023 10:10-10:55 Contact the reference group if you have feedback or suggestions for the course. |
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| Office hours | See table below. Times are tentative. |
| 22.11. | Wednesday | 09:15-10:00 | Auditorium F4, gamle fysikk |
| 01.12. | Friday | TBA | Zoom. (Espen in Stockholm) |
| 13.12. | Wednesday | 09:15-11:00 | Room 1148, SB2 (Espen's office) |
| 14.11. | Last lecture | Wednesday 15.11. |
| 08.11. | Exam dates | Monday December 4 and Friday December 15. Deadline November 10: Send me your preferred date by email to me. In case only one of the dates is good, let me know why. I may need to move some students to December 4. Dec 4: Johanne, Ulrik Dec 15: Jacob, Johanna, Robin, Peng, Sindre*, Maximillian, Torjei* |
| Project presentations | Monday 13.11. 14:15-16:00. (First hour. The second hour will be a lecture) Deadline November 13 12:00: Email slides (PDF) to me. Max 4.5 min and 5 slides + title slide per project. Schedule: 14:15-14:20 Johanna 14:20-14:25 Maximilian 14:25-14:30 Johanne 14:30-14:35 Peng 14:35-14:40 Robin 14:40-14:45 Jacob 14:45-14:50 Sindre 14:50-14:55 Ulrik 14:55-15:00 Torjei |
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| Last week | … of lectures: Week 46. Lectures: Monday 13.11. (incl. presentations) and Wednesday 15.11. (last lecture). No lecture Thursday 16.11. | |
| 30.10. | This week | Lectures as usual, Wednesday and Thursday. |
| Exam date | We discuss possible exam dates in the Thursday lecture (2.11.) | |
| Homework | Read yourselves: Note on Linear SDEs and Physical Brownian Motion by Krogstad. See 'General Information' in the menu. |
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| Exercise 5 Solutions 3 | Now posted, see 'Homework' in the menu. | |
| P11, Exercise 4 | Volunteer needed to write out the solution. Anyone up to the challenge? (I am happy to discuss the solution with you) |
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| 11.10. | Week 41 Week 42 Week 43 | This week - last week of lectures before project. (More lectures after). You work on project, no lectures. Espen in Spain. You work on project, no lectures. Extra office hours by Espen. |
| Project | Compulsory: To take the exam, you must prepare a small report about a topic related to stochastic differential equations not covered in the lectures. See 'Project' in the menu for detailed instructions and ideas of projects. |
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| Deadlines | October 13: email me your choice of project. December 1st: email me the written report. |
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| Supervision | Extra office hours: (Espen's office, room 1148, SB2) Wednesday 25.10. 9:00-10:30 and Thursday 26.10. 16:00-17:30 |
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| Read yourselves | Øksendal chp. 5.3 (discussion on weak solutions and uniqueness) | |
| Reference group | 2nd meeting today, see 'Reference group' in the menu for a super short summary. If there are other things you want to bring up, contact the reference group or me. |
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| Exercise 4/ Solutions 2 | Now posted, see'Homework' in the menu. | |
| Lecture plan | Updated until week 43. | |
| 28.09. | Extra lecture | Monday October 2nd, 14:15-16:00, room 656 SB2. I will post notes. |
| Office hours | Wednesdays 10:30-11:00. In my office, room 1148, SB2. |
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| Project | Weeks 42 and 43. See 'The Project' in the menu for detailed info and deadlines. | |
| Read yourselves | A comparison between Ito and Stratonovich integrals, Øksendal p 35-37. After Monday 2.10.: The Martingale representation theorem, Øksendal Theorem 4.3.4 (no proofs). |
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| Exercise 3 | Is now public, see 'Homework' in the menu. | |
| 16.09. | Lectures | I have decided to continue with the old schedule (Wednesday 8-10, Thursday 16-18). |
| Reference group | We have a reference group, see 'Reference group' in the menu. If you have feedback on the course, contact them (or me directly). |
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| First meeting Wednesday 20.09. at 10:05 (in my office, room 1148 SB2) | ||
| Exercise 2 | … and solutions to Exercise 1 posted. | |
| 11.09. | This week | Lectures according to old schedule. (Wednesday 8-10, Thursday 16-18) |
| 06.09. | Doodle | To determine whether we can move the lectures, I sent a Doodle on email to you. (Deadline Friday) |
| 30.08. | Slides/notes | I post notes from wednesday lectures (as long as there is a collision) and slides under 'Lectures' in the 'General information' in the menu. |
| Exercise 1 | Is now public, see 'Homework' in the menu. It covers more or less the 2 first weeks of curriculum. |
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| Todays lecture | The statement about measurability of compositions of functions was correct, see also my scanned notes. | |
| 21.08. | Lectures | No time-slot in the range 8-16 is good for all of you. I have therefore decided to try the following lecture times: |
| Wednesday | 08:15-10:00 | room 656, SB2 | collision for only 1 student, I will post notes |
| Thursday | 16:15-18:00 | room 656, SB2 | late, but no collisions |
| If better time slot become available, we will change. We will see next week. | ||
| Email updates? | You are safer if you sign up. Use this excel-sheet. | |
| Project | Compulsory, see 'The project' in the menu for more info. | |
| Exercises | There will be exercises, approximately every 2nd week. | |
| 20.06. | Info meeting | Monday August 21th, 14:15-15:00, at room 656 SB2. - Info about the course. - Decide on times for the lectures. - Set up email list for course. Cannot attend, but want to take the course? - Send me an email where you include the times you are not free (have other lectures). |
| Master student? | You can take the course either as MA8109 or TMA4505 (fordypningsemne). Grades: pass/fail in MA8109, A-F in TMA4505. 4th year MTFYMA students then take a regular course instead of TMA4505 in the 5th year. |