NMAB15025U Stochastic Processes 2
Volume 2016/2017
Education
BSc Programme in Actuarial 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.
Recommended Academic Qualifications
Mål- og integralteori
(MI)
Teaching and learning methods
5 hours of lectures and 3
hours of exercises per week for 7 weeks.
Workload
- Category
- Hours
- Exam
- 3
- Lectures
- 35
- Preparation
- 147
- Theory exercises
- 21
- Total
- 206
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Exam
- Credit
- 7,5 ECTS
- 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 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
- Censorship form
- No external censorship
One internal examiner.
- Re-exam
Same as ordinary exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAB15025U
- Credit
- 7,5 ECTS
- Level
- Bachelor
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Ernst Hansen (8-6c796f68757a6c754774687b6f35727c356b72)
phone 35 32 07 73, office 04.3.12,
Saved on the
09-03-2016