MAT9790 – Stochastic Filtering
Course description
Schedule, syllabus and examination date
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 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
MAT4720 - Stochastic analysis and stochastic differential equations
Overlapping courses
- 10 credits overlap with MAT4790 – Stochastic Filtering.
Teaching
4 hours lectures/exercises per week throught the semester.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
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 assignments 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: MAT4790 – Stochastic Filtering
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.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- 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.