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.

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination format: Written exam
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: Basic course in Mathematical Statistics

Course Occasion Information

Contact and Other Information

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