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.
Faculty
Organisational Unit
School of Mathematical Sciences
Chief examiner(s)
Associate Professor Yan Dolinsky
Coordinator(s)
Associate Professor Yan Dolinsky
Unit guides
Prerequisites
MTH3241 (or equivalent)
Co-requisites
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.
Synopsis
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.
Outcomes
On completion of this unit students will be able to:
- Develop specialised mathematical knowledge and skills within the theories of markov chains and random walks.
- Apply sophisticated stochastic modelling skills within a variety of contexts, from a wide range of scientific areas of knowledge.
- Apply critical thinking to problems in Markov chains in general, and in the theory of random walks in particular.
- 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.
Assessment
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