“I enjoyed the opportunity to study a course that is not available at my university and learn from specialist lecturers. It has helped to broaden my knowledge and gain exposure to as many different areas of mathematics as possible.”

Rachel Zhang, Australian National University

Stochastic Modelling

Lecturers

Dr Giang Nguyen, The University of Adelaide

Synopsis

Randomness is an important factor in modelling and analysing various-real life situations. This course covers some key aspects in stochastic modelling, including the theory underlying Brownian motions and diffusion processes, as well as techniques for numerical simulations.

Course Overview

  • Preliminaries from measure-theoretic probability
  • Modes of convergence
  • Brownian motion
  • Simulation algorithms
  • Filtration, martingales, and stopping times
  • Basics of Ito calculus

Prerequisites

  • Basic knowledge of stochastic processes (such as Markov chains) is desirable.

Assessment

  • Three assignments worth 10% each
  • One timed quiz worth 10%
  • Final exam worth 60%. This exam will be held at the students home institution.

Resources/pre-reading (if available)

Lecture notes will be provided during the course. Numerous books on Brownian motions will be of help, including:

  • M. Harrison, Brownian motion and stochastic flow systems, John Wiley & Sons, 1985.
  • T. Mikosch, Elementary Stochastic Calculus, World Scientific, 2002.

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Dr Giang Nguyen
The University of Adelaide

Dr Giang Nguyen is a Senior Lecturer in Applied Mathematics at the University of Adelaide. After receiving a PhD from the University of South Australia in 2009, she did her postdoctoral studies at the Universite libre de Bruxelles, Belgium, and the University of Adelaide until 2013. Her research interests include stochastic differential equations, Markov-modulated Brownian motions, stochastic fluid flows, matrix-analytic methods, branching processes, animal foraging, and energy systems.