Stochastic Processes 2
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
BSc Programme in Actuarial Mathematics
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.
Teaching and learning methods
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
Recommended prerequisites
Sandsynlighedsteori (Sand) - alternatively Mål- og integralteori (MI) from previous years.
Remarks
The course is similar to the course Advanced Probability Theory 1 (VidSand1) (NMAK11003U)
Feedback form
Written
Oral
Continuous feedback during the course
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.
Exam
- 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
- No external censorship
One internal examiner.
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course type
Single subject courses (day)
Workload
- Category
- Hours
- Lectures
- 35
- Preparation
- 146
- Theory exercises
- 21
- Exam
- 4
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAB15025U
- ECTS
- 7,5 ECTS
- Programme level
- Bachelor
- 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 (8-707d736c797e70794b786c7f73397680396f76)
phone 35 32 07 73, office 04.3.12,
Saved on the
28-02-2022
Are you BA- or KA-student?
Are you bachelor- or kandidat-student, then find the course in the course catalog for students:
Courseinformation of students
Courseinformation of students