Details for Course FMSF05F Probability Theory

Current Established Course Syllabus

General

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.

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.

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.

Judgement and Approach

Types of Instruction

Examination Formats

Admission Requirements

Assumed Prior Knowledge

Selection Criteria

Literature

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

Further Information

Course code

Administrative Information

1 course syllabus.

Valid from	First hand in	Second hand in	Established
Autumn 2020	2020‑05‑25 09:20:02	2020‑05‑25 09:21:25	2020‑08‑26

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