MA8109 Stochastic processes and differential equations

Fall 2017

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?

  • Differential equations with noisy/uncertain coefficients (stochastic differential equations), and their solutions, continuous time stochastic processes: We give a mathematical background, the main results, and some applications (more details in 'General Information' in the left menu).

    Of the multitude of applications in science, engineering and other disciplines, the most famous one is perhaps the Black-Scholes model for option pricing in finance.

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).


Date Title Message
23.11. Exam dates Date 1: December 6.

Date 2: December 12.

When is my
Check exam schedule below.

Exam format Oral exam, 45 min, questions and exercises.

Office hours Office hours before the exam in the table below.

Project deadline Send me the report by email by Friday 01.12.

Office hours before the exam
Date Time Room
Nonday 04.12. 14:15-15:00 Room 1148, SB2
Friday 08.12. 15:15-16:00 Room 1148, SB2
Monday 11.12. 09:15-10:00 Room 1148, SB2
Tuesday 12.12. Exam
Exam schedule
Day 1: Wednesday 06.12. room 656 SB2 Day 2: Tuesday 12.12. room 656 SB2
Time Time
13:15-14:00 08:15-09:00
14:05-14:50 09:05-09:50
14:55-15:40 09:55-10:40
12:20-13:00 Lunch
22.11. Final curriculum See 'General Information' in the left menu.

Reference group Last meeting in the break on Thursday (23.11.).

Summary and recommendations for the course?
Exam dates We discussed this in class last week and decided on oral exam on two different dates: 12.12. and 6.12.

PS: All students have accepted oral exam and the exam office is notified.
Problem set 5 Solutions published, see 'Homework' in the left menu.
08.11. OBS: Exam date We will choose one or two dates next Wednesday (Nov 15).

If you can not be present, send me an email with your available dates and the prefered dates.

Most likely we will have an oral exam.
Problem set 5 Now available along with solutions to Problem set 4.
26.10. Problem set 4 Now available.
Correction Recursion formula in Problem 9 in Problem set 2 has been corrected.
19.10. week 43 and 44

Projects: Independent work, no lectures.

Office hours during lecture times.

Counts for 20% of the grade.


Choice of project: Friday 20.10. (email to me)

— Submission of written report: Friday 01.12. (email to me).

All info in 'The project' in the left menu.
Reference group Meeting Thursday 19.10., see left menu.
Homework Read Øksendal Example 5.1.1 and chapter 5.3.
Existence of SDEs I just realized that an easier proof than I gave in the lectures can be found in Øksendal 6th ed. (my proof was from 5th ed.)

I encourrage you to learn this easier proof.
Solutions Problem set 3 Now available, see left menu. Many thanks to Stine who solved problems 4-6.
05.10. Problem set 3 Now available, see 'Homework' in left menu.
Volunteers We need volunteers to solve and tex the solutions of problems 4, 5, and 6.
25.09. Problem set 2 Now available, see 'Homework' in left menu.
07.09. Problem set 1 Now available, see 'Homework' in left menu.
Office hours Mondays 14:15-15:00, room 748 SB2
Lecture plan Updated for weeks 34-36.
I will update the plan continuously throughout the semester.
24.08. Week 34/35 Only lectures Thursday 24.08. and Wednesday 30.08.
Two lecture per week as of week 36.
OBS TMA4505! New rules this semester: If you want to take this course as TMA4505, then

(1) you register as a MA8109 student,

(2) you send me an email requesting TMA4505 code,

(3) I notify Sølvi Sønvisen at IE.
21.08. Lecture times Wednesday 14:15-16:00 in room 734 SB2.
Thursday 15:15-17:00 in room 734 SB2.
First lecture Thursday August 24, 15:15-17:00, room 734 SB2.
Want to attend? If you missed the info meeting, send me an email or drop by the lectures.
20.08. Info meeting Monday August 21th, 14:15-15:00, at room 734 SB2.
Master student? You can take the course either as MA8109 or TMA4505 (fordypningsemne).

Grades: pass/fail in MA8109, A-F in TMA4505.

Exam: Written or oral (NEW INFO: same exam for MA8109 and TMA4505).

4th year MTFYMA students then take a regular course instead of TMA4505 in the 5th year.
14:15-15:00  Lecture, 734 SB2  
15:15-16:00  Lecture, 734 SB2 
2018-02-12, Hallvard Norheim Bø