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.
lecture 3 hrs/week, workshop 1 hr/week
2 x in-class quizzes (30%), 2 x assignments (10%), final exam (60%)
(STAT2011 or STAT2911) and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933Prohibitions
STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT4021