Messages

Text and a suggested solution is available at the end of this page.

The grading process is now complete. It may take some days to go through the system. A solution to the exam is now available here or in Exams in the menu at the bottom of the page.

The distribution of results was as follows:

STK-MAT3710: A 14%, B 29%, C 14%, D 0%, E 14%, F29%.

STK-MAT4710: A 14%, B 29%, C 0%, D 43%, E 0%, F14%.

I hope you enjoyed the course and learnt a lot of probability theory! It was a pleasure!

Merry Christmas to everyone and good luck!

You can find the exam here or in the menu below.

The grading process takes no more than 3 weeks. Hopefully, we will be finished before Christmas. We will then publish a solution to the exam with grading criteria in this website.

Have a great Christmas time!

The lectures are finished and the lecture notes and the summary of the course are updated!

I have added a couple of exercises in Chapter 7 that were missing (the two last ones). I strongly recommend that you take a look at those two.

The exam will be next Friday 8th of December. Check here for information on time and location. Remember that no examination support material is allowed, not calculator either. You will not need it either.

The exam's structure will be:

Problem 1 (Theory): define or outline some concepts or results.

Problem 2 (Random variables): usual stuff about random variables and convergence.

Problem 3 (Conditional expectation): mainly conditional expectation, but it can also contain things from random variables as preparing steps.

The trial exam will be on Monday 20th of November, Auditorium 2 between 14:00 and 18:00. It is completely optional to do it.

I will upload the exam at 14:00 and facilitate physical printed copies and paper which will be placed on the first row. Bring your own approved calculator (not sure you need it actually) and pen.

The idea is that you sit and work on your own as if it were the real exam. Avoid using computer or any other aids. Do what you can. Thereafter, I will upload a solution with a grading system that you can use to correct your own, or someone else's exam.

The exam structure will be as follows: 4 problems.

Problem 1: of more theoretical nature. "Prove this or that property" or "state this or that concept/definition".

Problem 2: Random variables (general or convergence)

Problem 3: Conditional expectation

Problem 4: Martingales

Good luck!

Lecture notes are updated with the part dealing with stopping times and Doob's optional sampling theorem from last lecture.

A summary of the course (compact version of the lecture notes) has been uploaded, but it is not finished. I will add the last chapter when we finish it.

I have updated the lecture notes with today's theory on: supermartingales, submartingales and Doob decomposition (in discrete time with a proof) and the examples we went through (likelihood ratio, random walk, Brownian motion).

I have added some exercises at the end of Chapter 8 that you can try to solve.

See you on Wednesday!

The solution to the assignment is published. Everybody passed. You did all a great job!

I have uploaded the lecture notes with today's material. The exercise list from Chapter 6 has been modified a bit, so check the new numbering. The plan is to solve exercises: 6.5, 6.6, 6.10, 6.12, 6.13, 6.16 and 6.18, on Wednesday 25th of October.

Then, we will continue with exercises from Chapter 7 and then we go to the final chapter of this course: Chapter 8 on martingales.

Due to an event I must attend at the department, I feel obliged to cancel tomorrow's lecture. I am very sorry for this short notice. To compensate you, I have uploaded the lecture notes with Chapter 6 finished, with more exercises you can try to solve and also the things from Chapter 7 we did yesterday.

I will soon upload the solution to the assignment when the postponed deliveries are in place (around 19th of October).

See you then on Monday! Let me know if you have any questions.

Best regards,

David

The mandatory assignment is now available in the menu below. You can also reach it by clicking the word assignment, not this one, but this one: assignment.

Deadline is 12th of October, at 14:30. Delivery of the assignment in canvas: canvas.uio.no in a single pdf file.

Good luck!

Dear student,

Here is the information about the meeting with the group Risk and Stochastics that I talked about yesterday in the lecture. The target audience is bachelor students interested or curious about applications of probability theory, risk and stochastics and the master students from SMR.

This is a good opportunity to know the group, the topics of interest and what mathematics can be applied to in the industry. We will have an earlier student from the industry. There will be mingling and pizza! If you are in doubt... register!

Information and registration can be found here.

I have updated the lecture notes with some suggested solutions from Monday. In particular, I fixed Exercise 4.25 so that it makes full sense. I have also provided a thorough solution of Exercise 2.2 to amend the little mess at the beginning of the exercise. In any case, try to solve the exercises on your own with your own thoughts and writings.

Please, let me know if there is anything you miss or need. Tomorrow, there will be an extra session of exercise solving.

Best regards,

David

I feel obliged to cancel today's lecture as my voice has steadily gone away. I could probably offer something that one could call "a lecture" being very optimistic and it was hard to make the decision, but you deserve a real lecture, not just any mediocre lecture!

I had prepared to go through the following exercises today: 2.1, 2.2, 2.3, 2.4, 3.3, 3.4, 3.6, 3.11, 3.18, 3.19, 4.26 and 4.27.

Meet together, you may sit in the auditorium if it is available or somewhere else. Discuss and solve the exercises and send me an e-mail if you have questions! I can barely talk, but I can type!

See you on Monday. My deepest voiceless apologies for this short notice.

You can find an updated version of the lecture notes including today's lecture. You will also find a list of exercises at the end of Chapter 3.

The course has officially started and I am very happy that many of you came to the lecture! The language of the course will be English but remember that you can use any other Scandinavian language for the assignment and exam.

Your student representatives for this semester are:

Bret Lambert bretsl at uio.no

Sindre Jerpstad sindreje at uio.no

What happens next?

I have updated the lecture notes with the material from the lecture. You can find it in the menu below or by clicking here.

Every week I will update it. The first weeks I will go through some theory and then we will start solving exercises (they will also be included in the lecture notes). I will publish which exercises I will go through in the menu below. You can also find the list here. You can also suggest a specific exercise if you wish.

Welcome to the course!

Time and place: Our first lecture will take place on Wednesday 23rd of August at 10:15 am in Auditorium 4 in Vilhelm Bjerknes' hus (the building next to the Department of Mathematics). See the schedule of the course here.

The language of the course will be English unless everybody understands Norwegian, in such case it will be Norwegian. In any case, you may hand in your assignment and exam in English or any other Scandinavian language.

Literature/lecture material: We will use the following supporting book for this course: Jacod J., Protter P. Probability Essentials, 2nd Ed. 2004. Springer Berlin Heidelberg.

However, I will work out my own lecture notes progressively, which I will update every week with new content and exercises. There you will find...