Poisson Processes

Hardcover | May 1, 1987

byJ. F. C. Kingman

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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 ofmany 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.

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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 ofmany books. The other, the Poisson process, s...

J. F. C. Kingman is at University of Bristol.

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Format:HardcoverDimensions:112 pages, 9.21 × 6.14 × 0.47 inPublished:May 1, 1987Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198536933

ISBN - 13:9780198536932

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`The Poisson process is surely the most beautiful object in probability theory, and John Kingman is its most gifted expositor. One might have been forgiven for thinking that there would be little new to say, but in fact this book is studded with new and fascinating insights. It is rare tofind a book that simultaneously addresses the beginner and the expert. If there were a prize for the wisest probability book of the decade it would have to go to Bristol's Vice-Chancellor.'David Kendall, Cambridge, Journal of Royal Statistical Society, 1994