units

MTH5230

Faculty of Science

18 September 2017 11 December 2024

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This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

Monash University

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

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Associate Professor Kais Hamza

Offered

Clayton

  • Second semester 2016 (Day)

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:

  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.

Assessment

Weekly homework: 15%
Assignments: 15%
Exam: 70%

Workload requirements

Two 2-hour lectures per week

See also Unit timetable information

Chief examiner(s)

Associate Professor Kais Hamza

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.