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© 2017

Random Measures, Theory and Applications

Benefits

  • Presents a comprehensive account of modern random measure theory

  • Interesting for researchers in pure and applied probability theory

  • Very broad exposition

Book

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 77)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Olav Kallenberg
    Pages 15-48
  3. Olav Kallenberg
    Pages 49-69
  4. Olav Kallenberg
    Pages 70-108
  5. Olav Kallenberg
    Pages 109-153
  6. Olav Kallenberg
    Pages 154-210
  7. Olav Kallenberg
    Pages 211-265
  8. Olav Kallenberg
    Pages 266-309
  9. Olav Kallenberg
    Pages 310-346
  10. Olav Kallenberg
    Pages 347-405
  11. Olav Kallenberg
    Pages 406-446
  12. Olav Kallenberg
    Pages 447-480
  13. Olav Kallenberg
    Pages 481-537
  14. Olav Kallenberg
    Pages 538-621
  15. Back Matter
    Pages 622-694

About this book

Introduction

Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.

Keywords

60G57, 60G55 Palm and Gibbs kernels compensators convergence in distribution point processes random measures

Authors and affiliations

  1. 1.Auburn University Dept. MathematicsAuburnUSA

About the authors

Olav Kallenberg received his Ph.D. in 1972 from Gothenburg University. After holding various temporary research positions in Sweden and abroad, he emigrated in 1986 to the US, where he became a professor of mathematics at Auburn University. In 1977 he became the second recipient ever of the prestigious Rollo Davidson Prize, in 1989 he was elected a Fellow of the IMS, and in 1991-1994 he served as the editor of robability Theory and Related Fields. Kallenberg is the author of the previous books "Foundations of Modern Probability", and "Probabilistic Symmetries and Invariance Principles" along with numerous research papers in all areas of probability.

Bibliographic information

  • Book Title Random Measures, Theory and Applications
  • Authors Olav Kallenberg
  • Series Title Probability Theory and Stochastic Modelling
  • Series Abbreviated Title Probability and Stochastic (formerly: PIA & SMAP)
  • DOI https://doi.org/10.1007/978-3-319-41598-7
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-41596-3
  • Softcover ISBN 978-3-319-82392-8
  • eBook ISBN 978-3-319-41598-7
  • Series ISSN 2199-3130
  • Series E-ISSN 2199-3149
  • Edition Number 1
  • Number of Pages XXVIII, 680
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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Reviews

“The theory of random measures is an important point of view of modern probability theory. This is an encyclopedic monograph and the first book to give a systematic treatment of the theory. … the general theory presented in this book is therefore of great importance, far beyond the applications presented here. The book is bound to become the standard reference on the subject.” (Frank Aurzada, Mathematical Reviews, June, 2018)

“This book deals with a different aspects of the theory of random measures. … this is a useful book for a researcher in probability theory and mathematical statistics. It is very carefully written and collects results which are not easy to find in the literature or even forgotten.” (Nikolai N. Leonenko, zbMATH 1376.60003, 2018)