Poisson Processes

Erscheinungsjahr 1996
ISBN: 978-0-19-853693-2
Verlag: OUP Oxford

Buch, Englisch, Band 3, 112 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 331 g

Reihe: Oxford Studies in Probability

In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains.

This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context.

This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.

Autoren/Hrsg.

Kingman, J. F.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Stochastic models for random sets of points; Poisson processes in general spaces; Sums over Poisson processes; Poisson processes on the line; Marked Poisson processes; Cox processes; Stochastic geometry; Complete random measures; The Poisson-Dirichlet distribution.