Poisson Processes and Point Patterns
Semester II 2017-8
This course is for the
Taught Course Centre, with lectures
being broadcast interactively to collaborating universities
Lecture time and location
- Mondays 15:00 - 17:00.
- In Bath, the lecture theatre is 3W 4.13.
- The course runs for 8 consecutive weeks, starting on 15 January.
A point process is a probabilistic model for a collection of discrete objects, represented as `points' in space or discrete events in time. As such, point processes are relevant to many disciplines, such as astronomy, statistical physics, materials science, and the analysis of any kind of stochastic process with jumps.
The Poisson process is the basic building block in the theory of point processes, and is one of the most fundamental constructions in Probability, along with Brownian motion (although it has sometimes received less attention as an object of study in itself).
In this course we develop the mathematical theory of Poisson and other point processes. Much of the theory is presented in the abstract setting of an arbitrary measurable space, allowing for maximum generality.
`Lectures on the Poisson process', by Guenter Last and Mathew Penrose
(Cambridge University Press 2018). See
Other background reading
- `Poisson processes' by J.F.C. Kingman. This is an earlier textbook.
Provisional list of topics
The course will follow the main text (Last and Penrose); in particular material from Chapters 1-5, 8, 9, 12-15 as time permits. That is, we aim to cover topics from:
the Mecke equation and factorial measures,
Markings and mappings,
stationary point processes,
compound Poisson processes.