Prof Martin Anthony COL 3.13

This course is available on the BSc in Financial Mathematics and Statistics. 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 space, sigma‐algebra, probability measure, examples. Borel sigma-algebra, Lebesgue measure, Caratheodory's extension theorem. Random variables, distribution functions, discrete and absolutely continuous distributions, examples. Construction of the Lebesgue integral, relation to "measure‐ theoretic induction", convergence theorems, further properties, relation to Riemann integral. Different modes of convergence of random variables. Conditional expectation for simple, absolutely continuous and general random variables, construction and properties.

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

Students will be expected to produce 10 problem sets in the MT.

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

Other (100%).

Exam (100%) in the ST.