NMAK11003U Advanced Probability Theory 1 (VidSand1)

Volume 2013/2014
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
MSc Programme in Insurance Mathematics
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.
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. 
MI
5 hours of lectures and 3 hours of exercises per week.
  • Category
  • Hours
  • Exam
  • 3
  • Lectures
  • 35
  • Preparation
  • 147
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
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Aid
Written aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.