*Course Syllabus for*
# Probability Theory

Sannolikhetsteori

## FMSF05F, 7.5 credits

**Valid from:** Autumn 2020

**Decided by:** Professor Thomas Johansson

**Date of establishment:** 2020-08-26

## General Information

**Division:** Mathematical Statistics

**Course type:** Course given jointly for second and third cycle

**The course is also given at second-cycle level with course code:** FMSF05

**Teaching language:** English

## Aim

The course gives a deeper and extended knowledge of probability theory, useful for further studies in, e.g., extreme value theory and stochastic processes with applications.

## Goals

*Knowledge and Understanding*

For a passing grade the doctoral student must

- be able to explain different concepts in stochastic convergence and how they relate to each other,
- be able to explain the concepts of characteristic and moment generating functions and how these functions can be used,
- be able to describe the multi-dimensional normal distribution and the invariance properties under, e.g., linear combinations and conditioning,
- be able to explain the definition and basic properties of the Poisson process.

*Competences and Skills*

For a passing grade the doctoral student must
show the ability to integrate knowledge from the different parts of the course when solving problems.

## Course Contents

The course deepens and expands the basic knowledge in probability theory. Central moments in the course are transforms of distribution, conditional expectations, multidimensional normal distribution, and stochastic convergence. Further, the concept of stochastic processes is introduced by a fairly thorough treatment of the properties of the Poisson process.

## Course Literature

Gut, A.: An Intermediate Course in Probability Theory. Springer, 1995.

**Types of instruction:** Lectures, exercises

**Examination format:** Written exam

**Grading scale:** Failed, pass

**Examiner:**

## Admission Details

**Assumed prior knowledge:** Basic course in Mathematical Statistics

## Course Occasion Information

**Course coordinators:**

**Web page:** www.maths.lth.se/matstat/kurser/fmsf05/