Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Weak Convergence of Probability Measures

Practical information
Study year 2016/2017
Block 2
Programme level Full Degree Master
Course responsible
  • Ernst Hansen (8-68756b6471766871437064776b316e7831676e)
  • Department of Mathematical Sciences
Course number: NMAK16021U

Course content

        Weak convergence of probability measures on metric spaces,
        both separable and non-separable. Donsker's theorem on weak
        convergence of empirical distributions to Gaussian
        processes. Statistical applications.


Learning outcome


   * Convergence-concepts for probability measures on
     infinite-dimensional spaces

Skills: Ability to

   * prove and utilize uniform variants of the law of large numbers

   * Establish weak convergence to a stochastic process by combining
     weak convergence of finite dimensional distributions with
     combinatorical control.

   * use arguments based on chaining


Comptences: Ability to

   * explain the significans of working with smaller sigma-algebras
    than the Borel algebra on non-separable spaces, and master the
    corresponding technical complications.

   * derive asymptotic distributions for simple functionals of iid
     processes using weak convergence in function spaces.




Recommended prerequisites

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MSc Programme in Statistics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


---- SKEMA LINK ----

Teaching and learning methods

4 hours of lectures and 2 hours of exercises per week for 7 weeks. For
certain types of classes active participation is expected.


No restrictions/ no limitations




Category Hours
Lectures 28
Theory exercises 14
Preparation 133
Exam 31
English 206


Type of assessment

Oral examination, 30 min
with 30 min preparation time


All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Censorship form

No external censorship
Several internal examiners.


Same as ordinary

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