NMAB15025U  Stochastic Processes 2

Volume 2017/2018

BSc Programme in Actuarial Mathematics

  • Sequences of random variables, almost sure convergence, Kolmogorov's 0-1 law.
  • The strong law of large numbers.
  • Weak convergence of probability measures. Characteristic functions.
  • The central limit theorem. Triangular arrays and Lindebergs condition. The multivariate central limit theorem.
  • The ergodic theorem.
Learning Outcome


  • Fundamental convergence concepts and results in probability theory.

Skills: Ability to

  • use the results obtained in the course to verify almost sure convergence or convergence in law of a sequence of random variables.
  • verify conditions for the central limit theorem to hold.
  • translate between sequences of random variables and iterative compositions of maps.

Competences: Ability to

  • formulate and prove probabilistic results on limits of an infinite sequence of random variables.
  • discuss the differences between the convergence concepts.



Mål- og integralteori (MI)
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
Exam registration requirements

Approval of two assignments during the course is required to register for the exam.

All aids allowed

NB: If the exam is held at the ITX, the ITX will provide computers. Private computer, tablet or mobile phone CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.

Same as ordinary exam.

If the compulsory assignments were not approved before the ordinary exam they must be resubmitted at the latest two weeks before the beginning of the re-exam week. They must be approved before the re-exam.

Criteria for exam assesment

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

  • Category
  • Hours
  • Lectures
  • 35
  • Theory exercises
  • 21
  • Preparation
  • 147
  • Exam
  • 3
  • Total
  • 206