Lecturer(s): Prof Vassili Kolokoltsov
Prerequisite(s): ST342 Mathematics of Random Events or MA359 Measure Theory.
Commitment: 3 lectures/week, 1 tutorial/fortnight. This module runs in Term 2.
Content: Independence and conditioning, probability measures on metric spaces, types of probabilistic convergence, an introduction to martingales.
Aims: This course aims to give the student a rigorous presentation of some fundamental results in measure theoretic probability and an introduction to the theory of discrete time martingales. In so doing it aims to provide a firm basis for advanced work on probability and its applications.
Objectives: The objectives of the course are as follows: at the end of the course the student will:
- Understand the ideas relating to independence and zero-one laws and be able to apply these ideas in simple contexts.
- Understand the different modes of convergence for sequences of random variables (more generally random elements) and the relationship between these different modes.
- Be able to state and prove the Central Limit Theorem and understand how this result can be applied.
- Understand some basic results on discrete time martingales.
Assessment: 100% by 2-hour examination.
Course Material: Lecture notes, example sheets, and other module material are to be found at the Module Resources page. Note that lecture notes are made available progressively throughout the module.
You may also wish to see:
ST318: Resources for Current Students (restricted access)