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Unit of study_

STAT4021: Stochastic Processes and Applications

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. In this unit you will rigorously establish the basic properties and limit theory of discrete-time Markov chains and branching processes and then, building on this foundation, derive key results for the Poisson process and continuous-time Markov chains, stopping times and martingales. You will learn about various illustrative examples throughout the unit to demonstrate how stochastic processes can be applied in modelling and analysing problems of practical interest, such as queuing, inventory, population, financial asset price dynamics and image processing. By completing this unit, you will develop a solid mathematical foundation in stochastic processes which will become the platform for further studies in advanced areas such as stochastic analysis, stochastic differential equations, stochastic control and financial mathematics.

Code STAT4021
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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None
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 STAT3921
Assumed knowledge:
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Students are expected to have a thorough knowledge of basic probability and integral calculus and to have achieved at credit level or above in their studies in these topics

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 the limit theorems for discrete-time Markov chains to identify and interpret predictions of Markov chain models.
  • LO4. Explain Gambler's ruin problem and calculate extinction probability
  • LO5. Explain the properties of the Poisson and exponential distributions.
  • LO6. Construct a Poisson process and identify its single parameter from practical problem settings in a diverse range of applications.
  • LO7. Explain the definition of the continuous-time Markov chain based on discrete-time Markov chains and the Poisson process.
  • 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.