Prof Graham Brightwell

This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science 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.

Students must have completed Real Analysis (MA203).

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.

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

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

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

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