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
MSc Programme in Mathematics with a minor subject

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)

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
Type of assessment details
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

Kursusinformation

Language
English
Course number
NMAK11003U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 1
Schedulegroup
B
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Ernst Hansen   (8-6b786e6774796b744673677a6e34717b346a71)
phone 35 32 07 73, office 04.3.12,
Saved on the 28-02-2022

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