FSF3945 Advanced Probability 7.5 credits
Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3945 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
- Random walks and the heat equation
- Infinite divisibility
- Large deviations
- Weak convergence I
- Weak convergence
- Brownian motion
- Ergodic theory
Intended learning outcomes
After completing the course students are expected to:
- explain the connection between random walks and the heat equation
- explain in detail the properties of the Brownian motion
- have a good understanding of weak convergence in metric spaces
- outline the construction of the Brownian motion (Donsker's theorem) from random walks
- explain the main results and applications of ergodic theory
- have basic insights in additional topics (that may vary between years) in advanced probability
- be able to solve problems related to the theory
Literature and preparations
Specific prerequisites
Master’s degree in mathematics, applied mathematics or related field including at least 30 ECTS in mathematics.
Completed course in SF3940 or corresponding.
Recommended prerequisites
No information inserted
Equipment
No information inserted
Literature
- Greg Lawler, Random walk and the heat equation.
- Rick Durrett, Probability: Theory and Examples, 4th Edition, Cambridge Series in Statistical and Probabilistic Mathematics, 2010. ISBN 9780521765398
- Patrick Billingsley, Probability and Measure, 3rd Edition, Wiley.
- Patrick Billingsley, Convergence of Probability Measures, Wiley.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
P, F
Examination
- HEM1 - Home assignments, 3.5 credits, grading scale: P, F
- TENM - Oral exam, 4.0 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The examination will be done as a combination of homework and oral exam.
Other requirements for final grade
Homework and oral exam.
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
This course does not belong to any Main field of study.
Education cycle
Third cycle
Add-on studies
No information inserted
Contact
Henrik Hult (hult@kth.se)