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ST406: Applied Stochastic Processes with Advanced Topics

Lecturer(s): Dr Larbi Alili

Prerequisite(s): ST202 Stochastic Processes.

Commitment: 3 lectures per week, 1 example class per fortnight. This module runs in Term 1.

Availability: Only available to students who have not taken ST333

Aims: To provide an introduction to concepts and techniques which are fundamental in modern applied probability theory and operations research: Models for queues, point processes, and epidemics. Notions of equilibrium, threshold behaviour, and description of structure.

These ideas have a vast range of applications, for example routing algorithms in telecommunications (queues), assessment of apparent spatial order in astronomical data (stochastic geometry), description of outbreaks of disease (epidemics). We will only be able to introduce each area - indeed each area could easily be the subject of a course on its own! But the introduction will provide you with a good base to follow up where and when required. (For example: a MORSE student graduating in 1996 found the next year their firm was asking them to address problems in queuing theory, for which ST333 provided the basis.) We will discuss these and other applications and show how the ideas of stochastic process theory help in formulating and solving relevant questions.

Objectives: At the end of the course students will:

  • Be able to formulate continuous-time Markov chain models for applied problems.
  • Be able to use basic theory to gain quick answers to important questions (for example, what is the equilibrium distribution for a specific reversible Markov chain?).
  • Be able to solve for the transition probabilities for Markov chains on a finite state space.

Students will be given selected research material on advanced topics for independent study and examination.

Assessment: 10% by class test, 90% by examination.

There will be support classes associated with the course, and students will be expected to attend.

Class Tests: Class tests are scheduled for weeks 5 and 9 and will take place in one of the lectures.

Feedback: Feedback on class tests will be returned after 2 weeks, following each test.

You may also wish to visit:

ST406: Resources for Current Students (restricted access)