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The oral exam will be held in room 700 (7th floor in NHA building) on Thursday 17. and Friday 18. December. A schedule for the examination can be found in this course CANVAS room under announcements. 

Make sure that you note your time correctly, and that you arrive 15-20 minutes early.  

On the right hand side of this page (below the excersises panel) you will find a link to exam information. 

Read this note carefully! 

You are expected to prepare a 15 minutes presentation on a self chosen topic from the list of topics in the information sheet. After the presentation the examiners will ask questions regarding the presentation or about the remainder of the curriculum.

No support material is allowed to use under the presentati...

This week we will have two lectures where we will go through the curriculum of the course. This we will do by discussing different exercises, and topics from previous lectures at the blackboard. We will also look at the two exercises found on the semester page. 

You can attend both the Tuesday lecture and the Thursday lecture. Please bring at least one question/exercise or topic to discuss in class. 

You will also get the chance to try to write "something" on the blackboard, as a small exercise before the oral exam. 

We have two students in our class which takes the course as PhD sudents. They will each give a 30 min.  presentation on a topic of relevance for this course tomorrow (Friday 13. Nov) from 10.00 to 11.00. 

The two topics are: Martingale convergence, and L¨¦vy processes and L¨¦vy Kintchin decomposition. 

The presentations will be held using ZOOM. 

Please send me (Fabian) an email if you would like to attend, and I will distribute the zoom link. 

We have had some technical difficulties with the lecture videos. We have found the error, and have uploaded all the video lectures that had the error again. 

Please let us know if you experience any trouble with the video. 

/Fabian 

As discussed in class: Due to the Covid situation, the exam is now scheduled to be an oral examination over the dates 16.-18. December. 

Those of you that have an exam  December 15., please send me an email, and I will try to scheldule you for 18. December. 

The exact time schedule for the exam will be worked out during November. 

This week we will go back to the divided classroom lectures. That means that on both Tuesday and Thursday the same physical lecture will be given (on Girsanovs theorem). 

You are free to joiin one of the lectures, and you can choose which day suits you best. 

Since the Girsanov lecture is a bit shorter, feel free to bring some interesting exercises to class that you would like to solve together and discuss. 

The following exercises are relevant for the material on Ito integration and Ito's formula. 

Chp. 3 in ?ksendal: 3.1, 3.2, 3.3, 3.8 a), 3.16, 3.17, and 3.18

Chp. 4 in ?ksendal: 4.1 to 4.7, 4.8 a), 4.10, 4.11, 4.14, and 4.16. 

Remember that you are welcome to attend both lectures this week as well (both Tuesday 20. and Thursday 22. October), where we will cover lecture 7. Ito's formula. 

Remember that there will be two lectures this week, available for everyone. That is, tomorrow (13.10) we will go through Ito Integration part 1, and on Thursday (15.10) we will go through Ito integration part 2. 

You are welcome to attend both lectures at the usual lecture rooms. 

The student representative of this course is Vegard Enerstvedt, email: vegarene"at"math.uio.no . 

/Fabian 

Note: Typo in problem 6, B. It is now corrected. 

The mandatory assignment is now out! The link to the problem sheet is found on the right hand side of this page, below the lecture notes. 

You will have two weeks to complete the assignment, and hand in in Canvas. Deadline is Monday 12. October, at 23:59. 

Handing in this assignment is necessary in order to take the final exam in December. 

There will be no physical lectures during the period of the mandatory assignment. As mentioned in class, you are still expected to follow the video lectures, and I recommend that during the next two weeks you watch lecture 5 and 6. The week after the mandatory assignment we start again with physical lectures. Since there is not that many people in the classes at the moment, you are all welcome to attend both the Tuesday lecture and the Thursday lecture. We will in that week then go through both lecture 5 and lecture 6. ...

Here you can find 9 exercises (with solutions) on the topic of martingales, stopping times, and conditional expectation. 

I will go through some of the exercises in class, but encourage you to dry them out your self. This is also good practice for the upcoming mandatory assignment and for the exam.

/Fabian

Here is a list of exercises that is related to the curriculum of the different weeks: 

Week 1-3. Probability theory/stochastic processes:

Exercises 2.1.-20. in Chp. 2 of ?ksendal. 

(The first seven relates to probability, and the rest to stochastic processes).

As already mentioned; the physical lectures will have limited capacity. We will therefore divide the class, such that one half will be allowed to attend the classes on Tuesdays and the other on Thursdays.
These physical lectures will be reflections around the video lectures for the respective week. It is therefore very important that everyone watches the video lecture before attending the physical lecture. In addition, we will go through some practical examples, exercises and discuss some elements of proofs presented in the video lectures during the physical lectures.

We divide the class in the following way:

Tuesday lectures: Everyone with last name starting on a letter before M in the alphabet....

Due to the Corona situation, we will this year have a "flipped classroom". This means that all of the curriculum will be available for you as online videos, and the curriculum will be discussed at physical lectures once (possibly twice) a week. The videos  are created by  Dr. Torstein Nilssen at the University of Agder, and the physical lectures will be given by Dr. Fabian Harang at UiO.  

Depending on the number of students signed up for the course, we might need to divide the class in two, which means that one half will be invited to come for physical lectures at Tuesdays, while the other half will be invited for physical lectures on Thursdays. More information on this will come by email soon.

Video lectures offer the advantage of repeated viewings. We highly recommend using this advantage, e.g. by watching the videos before the physi...