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.
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
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 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
- Exam registration requirements
-
Approval of two assignments during the course is required to register for the exam.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
-
Same as ordinary exam.
If the compulsory assignments were not approved before the ordinary exam they must be (re)submitted. They must be approved at the latest three weeks before the beginning of the re-exam week.
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
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 (8-6a776d6673786a73457266796d33707a336970)
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