Lectures on the Poisson Process

Inhaltsverzeichnis

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. Characterizations 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 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.
Institute of Mathematical Stat Band 7

Lectures on the Poisson Process

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Beschreibung

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.

Details

Beschreibung

Details

  • Einband

    Taschenbuch

  • Erscheinungsdatum

    26.10.2017

  • Verlag Cambridge University Press
  • Seitenzahl

    314

  • Maße (L/B/H)

    22,9/15,4/1,9 cm

  • Gewicht

    457 g

  • Sprache

    Englisch

  • ISBN

    978-1-107-45843-7

Weitere Bände von Institute of Mathematical Stat

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  • 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. Characterizations 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 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.