Course Syllabus for students Autumn 2022

This course gives a solid background in and understanding of important results and methods in probability theory at an advanced level. The objective of the course is to give students a solid knowledge of important theorems within probability theory. The course should also enable them to apply advanced probability theory to building probability models in applications. Finally to be able to solve complicated probabilistic problems and explain various convergence concepts in probability

On completion of the course, the students will be able to:

1. Demonstrate a deep understanding of important theorems within probability theory.
2. Demonstrate a deep understanding of various convergence concepts in probability theory

3. To prove important theorems in probability theory
4. To solve advanced problems in probability theory

5. To critically apply central results in probability theory on typical probabilistic problems.

This course deals with random variables in one and several dimensions, conditional distributions, moment generating functions and characteristic functions, multivariate normal distributions, quadratic forms, order statistics, convergence criteria for random variables, the Borel-Cantelli lemmas, convergence via transforms, the central limit theorem and strong law of large numbers.

The course is designed as a series of lecturers and problem-solving sessions. Grading is based on individual performance via oral presentations and written hand ins.

The teaching is conducted in English.

Admitted to a doctoral program in statistics or a related subject of a recognized business school or university.

The course is graded Fail (U) or Pass (G).

Course assessment consists of two elements
• Oral presentation deals with ILOs 1,2,3,4,5
• Written assignments deals with ILOs 1,2,3,4,5
Each of these two elements must be passed to obtain a pass in the course.
The grades given are pass or fail.

A course evaluation will be conducted at the end of the course.

A. Gut, An Intermediate Course in Probability Theory, Springer-Verlag Second edition.
A. Gut, Probability: A Graduate Course Series: Springer Texts in Statistics. Second edition