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. This unit will establish basic properties of discrete-time Markov chains including random walks and branching processes. This unit will derive key results of Poisson processes and simple continuous-time Markov chains. This unit will investigate simple queuing theory. This unit will also introduce basic concepts of Brownian motion and martingales. Throughout the unit, various illustrative examples are provided in modelling and analysing problems of practical interest. By completing this unit, you will develop an essential basis for further studies stochastic analysis, stochastic differential equations, stochastic control, financial mathematics and statistical inference.

Code STAT3021 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? STAT2X11 None STAT3911 or STAT3011 or STAT3921 or STAT4021 Students are expected to have a thorough knowledge of basic probability and integral calculus

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.