MTH5230 - Markov chains and random walks - 2019

6 points, SCA Band 2, 0.125 EFTSL

Postgraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Associate Professor Kais Hamza


Associate Professor Kais Hamza

Unit guides



  • Second semester 2019 (On-campus)


MTH3241 (or equivalent)


Only students enrolled in the Master of Financial Mathematics can enrol in this unit. Exceptions can be made with permission from the unit co-ordinator.


Homogeneous Markov chains in finite and countable state space. Foster-Lyapunov criterion for recurrence and transience. Random walks in one and more dimensions. Polya theorem. Limit theorems: law of iterated logarithms, functional central limit theorem. Connections with the Brownian motion and the heat equation. Applications of random walks to finance and insurance.


On completion of this unit students will be able to:

  1. Develop specialised mathematical knowledge and skills within the theories of markov chains and random walks.
  2. Apply sophisticated stochastic modelling skills within a variety of contexts, from a wide range of scientific areas of knowledge.
  3. Apply critical thinking to problems in Markov chains in general, and in the theory of random walks in particular.
  4. Formulate expert solutions to practical financial, engineering or scientific problems using specialised cognitive and technical skills within the theories of markov chains and random walks.


NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Workload requirements

Two 2-hour lectures per week

See also Unit timetable information