Random processes (L.7) (862G1)
15 credits, Level 7 (Masters)
Topics covered include:
- After the introduction of the Poisson process, birth and death processes as well as epidemics models can be presented in full generality as applications of the pooled Poisson process. At the same time, you will be introduced to the Kolmogorov equations and to the techniques for solving them. Renewal theory is needed to better understand queues, and, for this reason, it is discussed before queues.
- A modern introductory course on stochastic processes must include at least a section on compound renewal processes (with a focus on the compound Poisson process) as well as a chapter on the Wiener process and on Ito stochastic calculus. This is necessary given the importance this process has in several applications from finance to physics. Modernisation is achieved by including a new introductory chapter divided into three parts.
- density and distribution of inter-event time
- pooled Poisson process
- breaking down a Poisson process
- applications of the Poisson process, e.g. birth-and-death processes, the Kolmogorov equations
- the ordinary renewal process
- the equilibrium renewal process
- the compound renewal process
- applications of renewal processes, queues.
- definition and properties
- introduction to stochastic integrals
- introduction to stochastic differential equations.
20%: Coursework (Portfolio, Problem set)
80%: Examination (Computer-based examination)
Contact hours and workload
This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.
We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2021/22. However, there may be changes to these modules in response to COVID-19, staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of material changes to modules at the earliest opportunity.
This module is offered on the following courses: