Random processes (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.


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.


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.


100%: Lecture


20%: Coursework (Problem Set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is 150 hours of work. This breaks down into 36 hours of contact time and 114 hours of independent study.

This module is running in the academic year 2017/18. 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.


This module is offered on the following courses: