Course content

The course provides an introduction to the stochastic filtering problem from stochastic analysis point of view. The objective of stochastic filtering is to estimate the state of a dynamical system from partial observations. This kind of problem arises everywhere, from telecommunications technology to mathematical finance.

Learning outcome

After having completed the course, you will:

  • understand the basic ingredients in the continuous time nonlinear stochastic filtering problem;
  • be familiar with the change of reference measure method;
  • be familiar with the Kallianpur-Striebel formula, the Zakai equation and the Kushner-Stratonovich equation;
  • know some numerical methods for solving the filtering problem, including particle filters.

In addition to the final examination, each PhD student 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 for the student to be admitted to the final examination.

Admission

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.

Prerequisites

Recommended previous knowledge

MAT4720 - Stochastic analysis and stochastic differential equations

Overlapping courses

10 credits overlap with MAT4790 – Stochastic Filtering

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

4 hours lectures/exercises per week.

Examination

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 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

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.

Evaluation

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

Credits

10

Level

PhD

Teaching

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Examination

The same semester as taught.

Teaching language

English

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