Poisson Processes and Point Patterns

Semester II 2017-8

Mathew Penrose (University of Bath)

This course is for the Taught Course Centre, with lectures being broadcast interactively to collaborating universities .

Lecture time and location

Course description

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.

Main textbook

Other background reading

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: