Stochastic Modelling

Lecturer

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 topics covers

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

Pre-requisites

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

Assessment

Four assignments worth 12.5% each, plus an exam at home worth 50%. This exam will be held at the students home institution.

Resources and Pre-reading

Lecture notes will be available. 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.
Stochastic Modelling

Biography

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.

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