Brownian Motion (BM)
Course content
- Weak convergence of probability measures. Characteristic functions.
- The central limit theorem. Triangular arrays and Lindeberg condition. The multivariate central limit theorem.
- Existence of a Brownian motion with continuous sample functions
- Sample path properties of Brownian motion: quadratic variation. non-differentiability, law of the iterated logarithm
- The strong Markov property for Brownian motion
- Optional sampling for Brownian motion
- Skorokhod embedding
- Weak convergence of random walks to Brownian motion
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject
MSc Programme in Mathematics-Economics
Knowledge:
- The fundamental role of Gaussian distributions and its rooting in CLT (central limit theorem)
- The basic framework of stochastic processes in continuous time
- Properties of Brownian motion
Skills: Ability to
- Establish weak convergence results in finite dimension and in separable metric spaces
- Derive explicit properties of Brownian motion using a variety of methods
Competencies: Ability to
- Produce independent proofs in extension of the acquired knowledge
5 hours of lectures and 3 hours of exercise class for 7 weeks.
Sand2 - alternatively VidSand1 (or Stok2) from previous years
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 30 minutes (30-minute preparation time)
- Exam registration requirements
-
To participate in the exam the compulsory assignment must be approved and valid
- Aid
- All aids allowed
All aids allowed during preparation
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
-
Same as ordinary exam.
If the compulsory assignment was not approved before the ordinary exam it must be (re)submitted and approved. It must be (re)submitted 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
- 149
- Theory exercises
- 21
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK24007U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 1
- Schedulegroup
-
B
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Ernst Hansen (8-68756b6471766871437064776b316e7831676e)
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Kursusinformation for indskrevne studerende