MTH5230 Markov chains and random walks
Faculty of Science
MTH5230 Markov chains and random walks is a level 5, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2027 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH5230
No prerequisites or corequisites besides the enrolment rules below.
After MTH5230
No unit lists MTH5230 as a prerequisite in the 2027 handbook.
Enrolment rules
COREQUISITE: Only students enrolled in the Master of Mathematics or the Master of Financial Mathematics can enrol in this unit. Exceptions can be made with permission from the unit coordinator.
Overview
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.
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should 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.
Workload and teaching
- Applied sessions11 hours
- Seminars36 hours
- Teaching approachActive learning
- Two 1.5-hour seminars;
- One 1-hour applied class (in weeks 2-12) and
- Eight hours of independent study per week.
Active learning will occur in lectures and applied classes.
Contacts
- Unit Coordinators
- Dr Ivan Guo
- Chief Examiners
- Dr Ivan Guo
Common questions
What are the prerequisites for MTH5230?
MTH5230 has no prerequisites, but enrolment rules apply.
When is MTH5230 offered?
In 2027, MTH5230 runs in Semester 2 at Clayton.
Does MTH5230 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.