ST318-15 Probability Theory

Introductory description

This module runs in Term 2 and is available for students on a course where it is a listed option and as an Unusual Option to students who have completed one of the prerequisite modules.

Pre-requisite(s): ST342 Mathematics of Random Events OR MA359 Measure Theory.
Leads to: ST401 Stochastic Methods in Finance, ST402 Risk Theory, ST403 Brownian Motion, ST411 Dynamic Stochastic Control

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Independence and zero-one laws
• Modes of convergence for sequences of random variables
• Limit theorems: law of large numbers (LLN) and central limit theorems (CLT)
• Conditioning and discrete time martingales

Learning outcomes

By the end of the module, students should be able to:

• understand the different modes of convergence for sequences of random and the relationship between these different modes;
• state and prove the Central Limit Theorem via the method of characteristic functions and understand how this result can be applied;
• understand some basic results on discrete -time martingales, including the martingale convergence theorem and optional stopping theorem, and show how these results can be used to obtain various characteristics of simple random walks.
• understand the ideas relating to independence and zero-one laws and be able to apply these ideas in simple contexts;

Indicative reading list

View reading list on Talis Aspire

Subject specific skills

TBC

Transferable skills

TBC