Stochastic Modelling

This subject has the following teaching availabilities in 2010:

One of

• 620-295 Real Analysis with Applications
• 620-158 Accelerated Mathematics 2

and one of

• 620-201 Probability
• 620-205 Probability for Statistics

Stochastic processes occur in finance as models for asset prices, in telecommunications as models for data traffic, in computational biology as hidden Markov models for gene structure, in chemistry as models for reactions, in manufacturing as models for assembly and inventory processes, in biology as models for the growth and dispersion of plant and animal populations, in speech pathology and speech recognition and many other areas.

This course introduces the theory of stochastic processes including Poisson processes, Markov chains in discrete and continuous time, and renewal processes. These processes are illustrated using examples from real-life situations. It then considers in more detail important applications in areas such as queues and networks (the foundation of telecommunication models), finance, and genetics.

After completing this subject students should:

• understand the basic concepts of random processes in discrete and continuous time;
• acquire an appreciation of how randomness and variability in time can be mathematically described using probability theory;
• be able to build, analyze and simulate basic stochastic models for simple real-life random phenomena evolving in time.

Two written assignments due mid-semester and at the end of semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).

K. Borovkov, Elements of Stochastic Modelling. World Scientific, Singapore, 2003.

This subject potentially can be taken as a breadth subject component for the following courses:

• Bachelor of Arts
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

• problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
• analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
• collaborative skills: the ability to work in a team;
• time-management skills: the ability to meet regular deadlines while balancing competing commitments.