Random processes (L.6) (G1101)

15 credits, Level 6

Spring teaching

Topics covered on this module include:

Poisson processes

  • density and distribution of into-event time
  • pooled Poisson process
  • breaking down a Poisson process
  • applications of the Poisson process, e.g. birth-and-death processes, the Kolmogorov equations.

Renewal processes

  • the ordinary renewal process
  • the equilibrium renewal process
  • the compound renewal process
  • applications of renewal processes, queues.

Rationalisation

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 Kolmogorov equations and the techniques for solving them.

Modernisation

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.

Wiener processes

  • definition and properties
  • introduction to stochastic integrals
  • introduction to stochastic differential equations.

Teaching and assessment

We’re currently reviewing teaching and assessment of our modules in light of the COVID-19 situation. We’ll publish the latest information as soon as possible.

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.

This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.