MAT9720 – Stochastic analysis and stochastic differential equations
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.
After completing the course you will:
- have a throrough understanding of stochastic methods that are inbetween 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, thecnology, 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.
PhD candidates from 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 - Lineær analyse med anvendelser / MAT4400 - Lineær analyse med anvendelser
- One of the following three courses will also give you an advantage, but it is not required to pass the course:
MAT2700 - Matematisk finans og investeringsteori
STK4510 - Innføring i finansmatematiske metoder og teknikker
- 10 credits overlap with MAT4720 – Stochastic analysis and stochastic differential equations
- 8 credits overlap with MAT4701 – Stochastic analysis with applications (continued)
- 8 credits overlap with MAT9701
- 4 credits overlap with STK4510 – Introduction to methods and techniques in financial mathematics (discontinued)
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department.
4 hours of lectures/exercises every week throughout the semester.
Final oral or written examination. The form of examination will be announced by the teaching staff by 15 October/15 March for the autumn semester and the spring semester respectively.
In addition, each PhD candidate is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.