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.
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Gunter 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. Mathew Penrose is Professor of Probability at the University of Bath. He is an internationally leading researcher in stochastic geometry and applied probability and is the author of the influential monograph Random Geometric Graphs (2003). He received the Friedrich Wilhelm Bessel Research Award from the Humboldt Foundation in 2008, and has held visiting positions as guest lecturer in New Delhi, Karlsruhe, San Diego, Birmingham, and Lille.
'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
'I have always considered the Poisson process to be a cornerstone
of applied probability. This excellent book demonstrates that it is
a whole world in and of itself. The text is exciting and
indispensable to anyone who works in this field.' Dietrich Stoyan,
Technische Universitat Bergakademie Freiberg , Germany
'Last and Penrose's Lectures on the Poisson Process constitutes a
splendid addition to the monograph literature on point processes.
While emphasizing the Poisson and related processes, their
mathematical approach also covers the basic theory of random
measures and various applications, especially to stochastic
geometry. They assume a sound grounding in measure-theoretic
probability, which is well summarized in two appendices (on measure
and probability theory). Abundant exercises conclude each of the
twenty-two 'lectures' which include examples illustrating their
'course' material. It is a first-class complement to John Kingman's
essay on the Poisson process.' Daryl Daley, University of
Melbourne
'Pick n points uniformly and independently in a cube of volume n in
Euclidean space. The limit of these random configurations as n is
the Poisson process. This book, written by two of the foremost
experts on point processes, gives a masterful overview of the
Poisson process and some of its relatives. Classical tenets of the
Theory, like thinning properties and Campbell's formula, are
followed by modern developments, such as Liggett's extra heads
theorem, Fock space, permanental processes and the Boolean model.
Numerous exercises throughout the book challenge readers and bring
them to the edge of current theory.' Yuval Peres, Microsoft
Research and National Academy of Sciences
'The book under review fills an essential gap and is a very
valuable addition to the point process literature. There is no
doubt that this volume is a milestone and will very quickly become
a standard reference in every field in which the Poisson process
appears.' Christoph Thale, MathSciNet
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