Measure Theoretic Probability

**This information is for the 2019/20 session.**

**Teacher responsible**

Dr Pavel Gapeev COL 4.10

**Availability**

This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

**Pre-requisites**

Students must have completed Real Analysis (MA203).

**Course content**

This is a first course in measure-theoretic probability. It covers the following topics. Abstract probability spaces: sample spaces, sigma-algebras, probability measures, examples. Borel sigma-algebra, Lebesgue measure. Random variables: distribution functions, discrete and absolutely continuous distributions, examples. Expectation and the Lebesgue integral: convergence theorems and properties. Different modes of convergence of random variables. Conditional expectation: definition, properties, examples. Changes of probability measure, Bayes' theorem.

**Teaching**

20 hours of lectures and 10 hours of classes in the MT.

**Formative coursework**

Written answers to set problems will be expected on a weekly basis.

**Indicative reading**

Comprehensive lecture notes will be provided.

The following books may prove useful:

D Williams, Probability with Martingales.

J. Jacod & P. Protter, Probability Essentials; A. Klenke Probability Theory. A Comprehensive Course

**Assessment**

Exam (100%, duration: 2 hours) in the summer exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: Unavailable

Average class size 2018/19: Unavailable

Capped 2018/19: No

Value: Half Unit

**Personal development skills**

- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills