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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_

STAT3021: Stochastic Processes

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 important properties and limit theorems of discrete-time Markov chain and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, such as the memoryless property, super positioning, thinning, Kolmogorov's equations and limiting probabilities. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modeling and analyzing 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.

Code STAT3021
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933)
Corequisites:
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None
Prohibitions:
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STAT3911 or STAT3011 or STAT3921 or STAT4021

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

  • LO1. explain and be able to apply the fundamentals 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. explain the basic properties of the Poisson process and use these to solve problems
  • LO6. construct a Poisson process and identify its parameter from practical problem settings
  • LO7. construct a continuous-time Markov chain and identify its generator from practical problem settings
  • LO8. explain the length in the queue and solve simple waiting time problems
  • LO9. explain definitions of Brownian and martingales
  • LO10. write proofs and apply the theory in diverse applications.

Unit outlines

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