Kursussøgning, efter- og videreuddannelse – Københavns Universitet

Videresend til en ven Resize Print Bookmark and Share

Kursussøgning, efter- og videreuddannelse

Advanced Probability Theory 1 (VidSand1)

Practical information
Study year 2016/2017
Time
Block 1
Programme level Full Degree Master
ECTS 7,5 ECTS
Course responsible
  • Ernst Hansen (8-6d7a7069767b6d764875697c7036737d366c73)
phone 35 32 07 73, office 04.3.12,
  • Department of Mathematical Sciences
Course number: NMAK11003U

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.

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.

 

 

Recommended prerequisites

Mål- og integralteori (MI)

Sign up


As an exchange, guest and credit student - click here!

Continuing Education - click here!

Education

MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economy

Studyboard

Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

A
---- SKEMA LINK ----

Teaching and learning methods

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

Capacity

No limit

Language

English

Workload

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

Exam

Type of assessment

Written examination, 3 hours under invigilation
---

Aid

All aids allowed

NB: If the exam is held at the ITX, the ITX will provide you a computer. 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

Criteria for exam assessment

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

Censorship form

External censorship

Re-exam

Same as ordinary exam

Mere information om kurset
Er du BA- eller KA-studerende?
Er du bachelor- eller kandidat-studerende, så find dette kursus i kursusbasen for studerende:

Kursusinformation for indskrevne studerende