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FSF3945 Advanced Probability 7.5 credits

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Information per course offering

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Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus FSF3945 (Spring 2019–)
Headings with content from the Course syllabus FSF3945 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  1. Random walks and the heat equation
  2. Infinite divisibility
  3. Large deviations
  4. Weak convergence I
  5. Weak convergence
  6. Brownian motion
  7. 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.

Literature

  1. Greg Lawler, Random walk and the heat equation.
  2. Rick Durrett, Probability: Theory and Examples, 4th Edition, Cambridge Series in Statistical and Probabilistic Mathematics, 2010. ISBN 9780521765398
  3. Patrick Billingsley, Probability and Measure, 3rd Edition, Wiley.
  4. Patrick Billingsley, Convergence of Probability Measures, Wiley.

Examination and completion

Grading scale

P, F

Examination

  • TENM - Oral exam, 4.0 credits, grading scale: P, F
  • HEM1 - Home assignments, 3.5 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.

If the course is discontinued, students may request to be examined during the following two academic years.

The examination will be done as a combination of homework and oral exam.

Other requirements for final grade

Homework and oral exam.

Examiner

Profile picture Henrik Hult

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

SCI/Mathematics

Education cycle

Third cycle

Postgraduate course

Postgraduate courses at SCI/Mathematics