MAT9720 – Stochastic analysis and stochastic differential equations

Schedule, syllabus and examination date

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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 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

Overlapping courses

*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.


mandatory assignment.

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.

Grading scale

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.

Facts about this course






Every autumn


Every autumn

Teaching language


The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.