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During 2021 we will continue to support students who need to study remotely due to the ongoing impacts of COVID-19 and travel restrictions. Make sure you check the location code when selecting a unit outline or choosing your units of study in Sydney Student. Find out more about what these codes mean. Both remote and on-campus locations have the same learning activities and assessments, however teaching staff may vary. More information about face-to-face teaching and assessment arrangements for each unit will be provided on Canvas.

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. After setting up basic elements of stochastic processes, such as time, state, increments, stationarity and Markovian property, this unit develops basic properties and limit theory of discrete-time Markov chains and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, stopping times and martingales. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modelling and analysing problems of practical interest. By completing this unit, you will develop the essential basis for further studies, such as stochastic calculus, stochastic differential equations, stochastic control and financial mathematics. Students who undertake the advanced unit MATH3921 will be expected to have a deeper, more sophisticated understanding of the theory in the unit and to be able to work with more complicated applications than students who complete the regular MATH3021 unit.

Code STAT3921
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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(STAT2011 or STAT2911) and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933
Corequisites:
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None
Prohibitions:
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STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021

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.

Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.