MAT9720 – Stochastic Analysis and Stochastic Differential Equations
Course description
Course content
The course gives a thorough basis for understanding stochatsic dynamics and models. We will in particular study Brownian motion and martingales, Ito’s stochastic calculus, stochastic integration and martingale representation theorems, Ito’s Formula. We will present stochastic dynamical models via stochastic differential equations and study existence and uniqueness of solutions, linear stochastic differential equations, theory for diffusion processes, Markov processes, Dynkin’s Formula, Girsanov’s Theorem. The course gives an introduction to the most common numerical methods for stochastic differential equations.
Learning outcome
After completing the course you will
- have a thorough understanding of stochastic methods that are in-between mathematical analysis and probability theory
- know how to use the fundamental tools in stochastic analysis
- be familiar with numerical methods for stochastic differential equations
- know how to use methods of stochastic analysis for modeling in different application areas like finance, industry, technology, biology, etc.
- be able to present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.
Admission to the course
PhD candidates from the Faculty of Mathematics and Natural Sciences at the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
- MAT3400 – Linear Analysis with Applications/MAT4400 – Linear Analysis with Applications
- It will also be an advantage to have taken the following courses:
Overlapping courses
- 10 credits overlap with MAT4720 – Stochastic Analysis and Stochastic Differential Equations.
- 10 credits overlap with MA374.
- 10 credits overlap with MAT4710 – Stochastic analysis II (discontinued).
- 10 credits overlap with M?105.
- 8 credits overlap with MAT4701 – Stochastic analysis with applications (continued).
- 6 credits overlap with MAT4711 – Stochastic analysis II (discontinued).
- 4 credits overlap with STK4510 – Introduction to methods and techniques in financial mathematics (discontinued).
- 4 credits overlap with MAT4700 – Stochastic analysis I (discontinued).
- 4 credits overlap with MAT9700 – Stochastic analysis I (discontinued).
Teaching
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Examination
Final written exam or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 1 October/1 March for the autumn semester and the spring semester respectively.
This course has 1 mandatory assignment that must be approved before you can sit the final exam.
In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4720 – Stochastic Analysis and Stochastic Differential Equations
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may submit your response in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- How to use AI as a student
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.