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MA411 Half Unit

Probability and Measure

**This information is for the 2024/25 session.**

**Teacher responsible**

Dr Pavel Gapeev

**Availability**

This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics and MSc in Quantitative Methods for Risk Management. This course is available as an outside option to students on other programmes where regulations permit.

**Pre-requisites**

Some background in real analysis is essential.

**Course content**

The purposes of this course are (a) to explain the formal basis of abstract probability theory, and the justification for basic results in the theory, and (b) to explore those aspects of the theory most used in advanced analytical models in economics and finance. The approach taken will be formal. Probability spaces and probability measures. Random variables. Expectation and integration. Convergence of random variables. Conditional expectation. The Radon-Nikodym Theorem. Bayes' formula. Martingales. Stochastic processes. Brownian motion. The Itô integral.

**Teaching**

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Autumn Term.

**Formative coursework**

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

**Indicative reading**

Full lecture notes will be provided. The following may prove useful: J S Rosenthal, A First Look at Rigorous Probability Theory; G R Grimmett & D R Stirzaker, Probability and Random Processes; D Williams, Probability with Martingales; M Caplinski & E Kopp, Measure, Integral and Probability; J Jacod & P Protter, Probability Essentials.

**Assessment**

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

** Key facts **

Department: Mathematics

Total students 2023/24: 12

Average class size 2023/24: 12

Controlled access 2023/24: No

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

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