Weak Convergence of Probability Measures

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.



MSc Programme in Statistics

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.




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

VidSand1 + VidSand2 or similar

7,5 ECTS
Type of assessment
Oral examination, 30 min
with 30 min preparation time
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.
Criteria for exam assessment

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

Single subject courses (day)

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