Gunter Last (Germany Karlsruhe Institute of Technology), Mathew Penrose (University of Bath)

Lectures on the Poisson Process

• Broschiertes Buch

Produktbeschreibung

This self-contained introduction to the Poisson process covers basic theory and certain advanced topics in the setting of a general abstract measure space. The text includes applications and numerous exercises, and is ideal for graduate courses or self-study by mathematicians, physicists, and engineers.

Produktdetails

• Institute of Mathematical Statistics Textbooks
• Verlag: Cambridge University Press
• Seitenzahl: 314
• Erscheinungstermin: 26. Oktober 2017
• Englisch
• Abmessung: 229mm x 152mm x 18mm
• Gewicht: 450g
• ISBN-13: 9781107458437
• ISBN-10: 1107458439
• Artikelnr.: 48579946

Autorenporträt

Günter Last is Professor of Stochastics at the Karlsruhe Institute of Technology, Germany. He is a distinguished probabilist with particular expertise in stochastic geometry, point processes, and random measures. He coauthored a research monograph on marked point processes on the line as well as two textbooks on general mathematics. He has given many invited talks on his research worldwide.

Inhaltsangabe

Preface; List of symbols; 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; References; Index.

Rezensionen

'An understanding of the remarkable properties of the Poisson process is essential for anyone interested in the mathematical theory of probability or in its many fields of application. This book is a lucid and thorough account, rigorous but not pedantic, and accessible to any reader familiar with modern mathematics at first degree level. Its publication is most welcome.' J. F. C. Kingman, University of Bristol