SF2944 Foundations of Probability Theory 7.5 credits

-Basic concepts: Probability spaces, Kolmogorov axioms, random variables, distributions.

-Expectation: Integration with probability measures, dominated and monotone convergence theorems, Markov inequality.

-Independent algebras and random variables, Borel-Cantelli lemma.

-Weak law of large numbers: L2-convergence, convergence in probability, weak law of large numbers.

-Strong law of large numbers: Almost sure convergence, Kolmogorov's law.

-Weak convergence: Convergence in distribution, characteristic function, Lévy's continuity theorem, central limit theorem. 

-Conditional expectation: conditional expectation and variance, martingales, Doob inequalities and martingale convergence.

The overall aim of the course is for the students to become well acquainted with fundamental concepts, theorems and solution methods of probability theory.

After the course the student should be able to:

-formulate central definitions and theorems within the subject area of the course;

-apply and generalize methods within the subject area of the course;

-read and understand a mathematical text, in order to learn how to solve problems involving proofs of basic concepts within probability theory.

English B / English 6

Completed course in Probability theory and statistics (SF1918, SF1922 or similar)

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

• TEN1 - Written exam, 7.5 credits, grading scale: A, B, C, D, E, FX, 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.

• 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.