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.
3 lectures per week, tutorial 1hr per week.
2 x Quiz (2 x 15%), 2 x Assignment (2 x 5%), Final Exam (60%)
STAT2X11 and (MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933)Prohibitions
STAT3911 or STAT3011