An Introduction to the Theory of Point Processes

Volume II: General Theory and Structure

  • D. J. Daley
  • D. Vere-Jones

Part of the Probability and Its Applications book series (PIA)

Table of contents

About this book

Introduction

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present An Introduction to the Theory of Point Processes in two volumes with subtitles Volume I: Elementary Theory and Methods and Volume II: General Theory and Structure.

Volume I contains the introductory chapters from the first edition together with an account of basic models, second order theory, and an informal account of prediction, with the aim of making the material accessible to readers primarily interested in models and applications. It also has three appendices that review the mathematical background needed mainly in Volume II.

Volume II sets out the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

D.J. Daley is recently retired from the Centre for Mathematics and Applications at the Australian National University, with research publications in a diverse range of applied probability models and their analysis; he is coauthor with Joe Gani of an introductory text on epidemic modelling. The Statistical Society of Australia awarded him their Pitman Medal for 2006.

D. Vere-Jones is an Emeritus Professor at Victoria University of Wellington, widely known for his contributions to Markov chains, point processes, applications in seismology, and statistical education. He is a fellow and Gold Medallist of the Royal Society of New Zealand, and a director of the consulting group Statistical Research Associates.

Keywords

Martingal Martingale ergodic theory point process random measure

Authors and affiliations

  • D. J. Daley
    • 1
  • D. Vere-Jones
    • 2
  1. 1.Centre for Mathematics and its Applications Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  2. 2.School of Mathematics, Statistics and Computing ScienceVictoria University of WellingtonWellingtonNew Zealand

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-49835-5
  • Copyright Information Springer-Verlag New York 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-21337-8
  • Online ISBN 978-0-387-49835-5
  • Series Print ISSN 1431-7028
  • About this book