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Institut für Stochastik

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Kollegiengebäude Mathematik (20.30)
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Karlsruher Institut für Technologie
Institut für Stochastik

Englerstr. 2
D-76131 Karlsruhe

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D-76128 Karlsruhe

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Lectures on the Poisson Process

by Günter Last and Mathew Penrose.

PDF file of the book (xiv + 287 pages), preliminary version of 23 February 2017.

Commercial reproduction prohibited.
To be published as IMS Textbook by Cambridge University Press.

Please send comments to guenter.last@kit.edu or to M.D.Penrose@bath.ac.uk.


Contents:

Preface
1. The Poisson distribution
2. Point processes
3. Poisson processes
4. Factorial measures and the Mecke equation
5. Mappings, markings and thinnings
6. Characterizations of the Poisson process
7. Poisson processes on the real line
8. Stationary point processes
9. Palm distributions of simple point processes
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 representation
19. Perturbation analysis
20. Covariance identities
21. Normal approximation of Poisson functionals
22. Normal approximation in the Boolean model
Appendix A: Some measure theory
Appendix B: Some probability theory
Appendix C: Historical notes
References
Index