Prof Graham Brightwell

This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. 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).

Experience obtained through other Mathematics and Statistics courses is highly desirable. 

The purposes of this course are (i) to explain the formal basis of abstract probability theory, and the justification for basic results in the theory, and (ii) 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. Markov chains. Convergence of random variables. Conditional expectation and martingales, in the discrete case.

20 hours of lectures and 10 hours of classes in the MT. 2 hours of lectures in the ST.

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

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

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