Module Catalogue 2026/27

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

To develop a knowledge and appreciation of Markov processes in continuous time and their
application to stochastic mathematical modelling.

The modelling of many biological and physical systems is often naturally done in continuous time.
Markov processes are the most important family of stochastic processes which evolve in
continuous time and have been widely used, with applications in areas such as epidemiology,
ecology, chemical reactions and statistical physics. We will encounter mathematical tools for
building and analysing stochastic processes in continuous time, and use them to consider some of
these applied examples.

Outline Of Syllabus

Review of Poisson processes and the exponential distribution. Markov processes on discrete state
spaces: transition probabilities, rate matrices, and the Kolmogorov equations. Stationary
distributions, reversibility and detailed balance. The case of finite state space. Birth-death models.
Dwell times and stochastic simulation algorithms. Multivariate Markov processes: models of
epidemics and predator-prey populations.

Intended Knowledge Outcomes

At the end of the module it is expected that a student will be able to:
* Outline the key concepts underpinning stochastic processes on discrete data which evolve over
continuous time.
* Analyse models to derive key properties such as stationarity and reversibility.
* Describe a variety of models for specific scientific applications.

Intended Skill Outcomes

At the end of the module it is expected that a student will be able to:
* Formulate and solve problems that relate to continuous time stochastic processes.
* Use the properties of Markov processes and associated algorithms to perform exact and
approximate simulation of processes for a variety of applications.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition):
remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

N/A

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
The coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.
Note: the exam for MAS8717 is more challenging than the exam for MAS3931.

General Notes

N/A