MAT9720 – Stochastic Analysis and Stochastic Differential Equations

Schedule, syllabus and examination date

Choose semester

Teaching and exams spring 2022

In light of the most recent infection control regulations, we will at the start of the spring semester 2022 increase our online teaching, while we at the same time try to maintain in-person teaching where this is possible. We hope to go back to more in-person teaching later on in the semester. You will be informed about any changes in teaching or examinations on the semester page, in Canvas or through your regular channels.

Read more about postponed exams for the autumn semester 2021.

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.

Overlapping courses

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 15 October/15 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:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Jan. 17, 2022 12:26:45 AM

Facts about this course

Credits
10
Level
PhD
Teaching
Autumn
Examination
Autumn
Teaching language
English