STK9210 - Convergens of Probability Measures

Course content

The concepts and machinery associated with convergence in probability and in distribution are lifted from the finite-dimensional Euclidean cases to more abstract spaces, and, specifically, to spaces C and D of functions from the unit interval to the real line. This leads to a framework for construction of and convergence of stochastic processes. Topics include Donsker's theorem, invariance principles, tightness of sequences of measures, empirical processes, Brownian motion and Brownian bridges, and convergence to Poisson type processes. Applications to problems in theoretical statistics and probability theory are given.

Learning outcome

The student learns methodology for proving convergence and approximations of various empirical processes of importance in theoretical statistics and probability theory.

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

STK4010 - Asymptotic theory (discontinued) or working knowledge at a similar level. Master's degree in statistics, or working knowledge on a similar level.

Overlapping courses

For information about the potential partial overlap with other courses, contact the Department.

Teaching

Each week, two hours of lectures plus one hour of exercises. If a small number of students are following the course, it may be organised on a self-reading basis, with one weekly hour of joint or individual supervision.

Examination

Depending on the number of students, the exam will be in one of the following four forms:
1. Only written exam
2. Only oral exam
3. A project paper followed by a written exam.
4. A project paper followed by an oral exam/hearing.
For the latter two the project paper and the exam counts equally and the final grade is based on a general impression after the final exam. (The two parts of the exam will not be individually graded.)

What form the exam will take will be announced by the teaching staff within October 15th for the autumn semester and March 15th for the spring semester.

Examination support material

Permitted aids at the exam if written: Approved calculator.
Oral exam: No aids permitted.

Information about approved calculators (Norwegian only)

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

This course offers both postponed and resit of examination. Read more:

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. If you want to attend the course, please send an e-mail to studieinfo@math.uio.no.

Examination

According to demand and resources.

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.