Advanced Probability Theory 1 (VidSand1)

Course content

  • 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.
Education

MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics
MSc Programme in Mathematics-Economics
MSc Programme in Statistics
 

Learning outcome

Knowledge:

  • 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.

 

 

5 hours of lectures and 3 hours of exercises per week for 7 weeks.

Sandsynlighedsteori (Sand) - alternatively Mål- og integralteori (MI) from previous years.

Academic qualifications equivalent to a BSc degree is recommended.

The course is similar to Stochastic Processes 2 (NMAB15025U).
It is not recommended to follow both courses.

Written
Oral
Continuous feedback during the course of the semester

Written feedback in the form of comments to the compulsory
assignements.

Oral feedback during exercise classes, as a response to the
contribution of the students to the solution process of the
exercises.

 

ECTS
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
Skriftlig prøve
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
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
  • 35
  • Preparation
  • 146
  • Theory exercises
  • 21
  • Exam
  • 4
  • English
  • 206