Poisson Processes
Series: Oxford Studies in Probability; 3;
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45 864 Ft
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Product details:
- Publisher Clarendon Press
- Date of Publication 17 December 1992
- ISBN 9780198536932
- Binding Hardback
- No. of pages112 pages
- Size 242x163x12 mm
- Weight 349 g
- Language English
- Illustrations line figures 0
Categories
Short description:
In the theory of random processes there are two that are fundamental- one, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight less worthy of study in its own right and has been largely neglected in the literature. 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.
MoreLong description:
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.
'provides an enjoyable and clearly written introduction to the structure and properties of Poisson processes ... Thanks to skillful steering away from, and around, technicalities, it is widely accessible. If you don't know the story, read this book - you will then know what you are missing. If you do know it, a browse through the book, particularly the later chapters, is still worthwhile for interesting perspectives on several areas.'
P.J. Donnelly, Queen Mary and Westfield College, Short Book Reviews (Publication of the International Statistical Institute)
Table of Contents:
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.
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