MATM30F

Temporary

Mathematical Foundations of Probability

7.5

Course given jointly for second and third cycle

7151 (Centre of Mathematical Sciences / Mathematics)

 -11-15

Professor Thomas Johansson

English

Every autumn semester

The aim of the course is to give mathematical knowledge that facilitates successful studies in probability, stochastic processes and stochastic differential equations. These subjects are becoming more and more important in many applications, such as meteorology, finance and social planning.

The course deepens and extends basic knowledge in probability theory. A central part of the course is existence and uniqueness theorems about measures defined on sigma-algebras, integration theory, conditional expectation and weak convergence in metric spaces.

be able to explain the measure theoretic approach to probabilities and random variables;

be able to explain the construction of the Lebesgue-integral and the fundamental convergence theorem for this integral;

be able to explain how the concepts conditional expectation and weak convergence can be formalized through measure theory.

be able to use the fundamental theorems in integration theory to solve problems;

be able to choose an appropriate solution strategy for a problem within the course's range, and thereafter work out a detailed solution.

Lectures

Exercises

Oral exam

Failed, pass

Linear algebra, calculus in one and several variables, and basic courses in Fourier analysis and mathematical statistics.

Probability. Springer Science & Business Media, 1996. ISBN 9780387945491.

MATM30F

 -11-15

Professor Thomas Johansson