Lectures on the Poisson Process
by Günter Last and Mathew Penrose.
PDF file of the book (xiv + 293 pages), version of 21. August 2017.
Commercial reproduction prohibited.
Published by Cambridge University Press, 2017 (IMS Textbook).
Please send comments to firstname.lastname@example.org or to M.D.Penrose@bath.ac.uk.
1. Poisson and other discrete distributions
2. Point processes
3. Poisson processes
4. The Mecke equation and factorial measures
5. Mappings, markings and thinnings
6. Characterisations of the Poisson Process
7. Poisson processes on the real line
8. Stationary point processes
9. The Palm distribution
10. Extra heads and balanced allocations
11. Stable allocations
12. Poisson integrals
13. Random measures and Cox processes
14. Permanental processes
15. Compound Poisson processes
16. The Boolean model and the Gilbert graph
17. The Boolean model with general grains
18. Fock space and chaos expansion
19. Perturbation analysis
20. Covariance identities
21. Normal approximation
22. Normal approximation in the Boolean model
Appendix A: Some measure theory
Appendix B: Some probability theory
Appendix C: Historical notes