Abstract

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in an appendix. The authors are well-known researchers in probability theory, especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.
Original languageEnglish
PublisherCambridge University Press
Number of pages313
ISBN (Print)978-1-107-08801-6
Publication statusPublished - 21 Dec 2017

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Stochastic Geometry
Poisson process
Boolean Model
Stochastic Analysis
Measure space
Stationary point
Probability Theory
Point Process
Stationary Process
Hyperplane
Exercise
Graph in graph theory
Experience
Sound
Object
Text
Teaching
Background
Knowledge

Cite this

Last, G., & Penrose, M. (2017). Lectures on the Poisson Process. Cambridge University Press.

Lectures on the Poisson Process. / Last, Günter; Penrose, Mathew.

Cambridge University Press, 2017. 313 p.

Research output: Book/ReportBook

Last, G & Penrose, M 2017, Lectures on the Poisson Process. Cambridge University Press.
Last G, Penrose M. Lectures on the Poisson Process. Cambridge University Press, 2017. 313 p.
Last, Günter ; Penrose, Mathew. / Lectures on the Poisson Process. Cambridge University Press, 2017. 313 p.
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