Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Stochastic Processes 2

Practical information
Study year 2016/2017
Time
Block 1
Programme level Bachelor
ECTS 7,5 ECTS
Course responsible
  • Ernst Hansen (8-6e7b716a777c6e7749766a7d7137747e376d74)
phone 35 32 07 73, office 04.3.12,
  • Department of Mathematical Sciences
Course number: NMAB15025U

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)

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Education

BSc Programme in Actuarial Mathematics

Studyboard

Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

A
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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
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Aid

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

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

No external censorship
One internal examiner.

Re-exam

Same as ordinary exam.

Mere information om kurset
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