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 modeling 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.
lecture 3 hrs/week, workshop 1 hr/week
2 x homework assignments (10%), 2 x in-class quizzes (30%), final exam (60%)
STAT2011 or STAT2911, and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 or equivalent. That is, 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.
STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT3921.