Poisson Processes
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.
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Poisson Processes
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.
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Poisson Processes

Poisson Processes

by J. F. C. Kingman
Poisson Processes

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.
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