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Unit of study_

STAT3921: Stochastic Processes (Advanced)

A stochastic process is a mathematical model of time-dependent random phenomena and is employed in numerous fields of application, including economics, finance, insurance, physics, biology, chemistry and computer science. This unit will establish basic properties of discrete-time Markov chains including random walks and branching processes. This unit will derive key results of Poisson processes and simple continuous-time Markov chains. This unit will investigate simple queuing theory. This unit will also introduce basic concepts of Brownian motion and martingales. Throughout the unit, various illustrative examples are provided in modelling and analysing problems of practical interest. By completing this unit, you will develop a solid mathematical foundation of stochastic processes for further studies in advanced areas such as stochastic analysis, stochastic differential equations, stochastic control, financial mathematics and statistical inference. Students who undertake STAT3921/4021 will be expected to have a deeper, more sophisticated understanding of the theory and to be able to work with more complicated applications than students who complete the regular STAT3021 unit.

Code STAT3921
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021
Assumed knowledge:
Students are expected to have a thorough knowledge of basic probability and integral calculus and to have achieved at credit level or above

At the completion of this unit, you should be able to:

  • LO1. Explain and apply the theoretical concepts of probability theory and stochastic processes.
  • LO2. Construct a discrete-time Markov chain and identify its transition probability matrix from practical problem settings.
  • LO3. Explain and be able to apply limit theorems of discrete-time Markov chains and use those to identify and interpret their stationary distribution
  • LO4. Explain Gambler's ruin problem and calculate extinction probability
  • LO5. Construct a Poisson process and identify its parameter from practical problem settings in a diverse range of applications.
  • LO6. Explain the basic properties of the Poisson process and use these to solve problems.
  • LO7. Construct a continuous-time Markov chain and identify its generator in settings of practical problems in a diverse range of applications.
  • LO8. Explain the length in the queue and solve simple waiting time problems
  • LO9. Explain definitions of Brownian and martingales
  • LO10. Write clear, complete and logical proofs for mathematical hypotheses that are new to the student.