MT4528 Markov Chains and Processes

Academic year

2025 to 2026 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

11.00 am Mon (weeks 2, 4, 7, 9, 11), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr R C Pinto Borges

Dr R C Pinto Borges
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Rui Borges

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module provides an introduction to the theory of stochastic processes and to their use as models, including applications to population processes and queues. The syllabus includes the Markov property, Chapman-Kolmogorov equations, classification of states of Markov chains, decomposition of chains, stationary distributions, random walks, branching processes, the Poisson process, birth-and-death processes and their transient behaviour, embedded chains, Markovian queues and hidden Markov models.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2504

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (weeks 1 - 10) and 8 tutorials over the semester.

Scheduled learning hours

33

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

117

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Define and understand general aspects of discrete and continuous time Markov processes
  • Use directed graphs and transition probability matrices to classify and understand the states of Markov chains
  • Calculate various properties of Galton-Watson processes
  • Apply theorems related to birth and death processes to queuing systems
  • Define Poisson processes and demonstrate some of their properties
  • Grasp the fundamental aspects of hidden Markov models