Poisson Processes

by J. F. C. Kingman

Overview

Two fundamental theories are commonly debated in the study of random processes: the Bachelier Wiener model of Brownian motion, which has been the subject of many books, and the Poisson process. While nearly every book mentions the Poisson process, most hurry past to more general point processes or to 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 contexts. This book attempts to redress the balance. It records the author'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.

Product Details

ISBN-13:	9780198536932
Publisher:	Oxford University Press
Publication date:	01/28/1993
Series:	Oxford Studies in Probability , #3
Edition description:	New Edition
Pages:	112
Product dimensions:	9.32(w) x 7.70(h) x 0.54(d)

About the Author

University of Bristol

Table of Contents

1. Stochastic Models for Random Sets of Points2. Poisson Processes in General Spaces3. Sums Over Poisson Processes4. Poisson Processes on the Line5. Marked Poisson Processes6. Cox Processes7. Stochastic Geometry8. Complete Random Measures9 The Poisson-Dirichlet Distribution.

Editorial Reviews

"Fulfills the expectations one might have when a famous elder author writes a book on a classic topic. It gives the basic facts in a clear and lucid way. It is shown how the theory can be applied to interesting problems of astronomy, queuing and traffic, etc., and these examples are studied very thoroughly and deeply, giving even the specialist new insights . . . . an excellent basis for lectures or seminars . . . a valuable gift for a young mathematician to stimulate his or her interest in stochastic processes and in applied probability in general." —Dietrich Stoyan, Mathematical Reviews

"Whereas treatises on Brownian motion abound, there is a dearth of parallel treatments of the Poisson process. In point of fact, this book is the very first. We read it from cover to cover as soon as we received it, like a novel, and we felt refreshed by it."—The Bulletin of Mathematics Books

"It is a rare thing for a mathematical book to attract by the sheer fascination of its narrative. Here is one that can be read and enjoyed as an unfolding story, recounting the highlights of a journey through a memorable landscape....I can almost recommend it as enchanting bedtime reading....In the hundred or so pages of the book the reader does indeed get a feeling of the beauty and power of the Poisson process....The book succeeds admirably in its aim of shining a spotlight on many of the arresting features of the Poisson process in quick succession...It is a pity we do not have many more mathematical books written in the refreshing style of this one."—Stochastics and Stochastics Reports

From the Publisher