Branching Processes

  • Krishna B. Athreya
  • Peter E. Ney

Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 196)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Krishna B. Athreya, Peter E. Ney
    Pages 1-65
  3. Krishna B. Athreya, Peter E. Ney
    Pages 66-101
  4. Krishna B. Athreya, Peter E. Ney
    Pages 102-136
  5. Krishna B. Athreya, Peter E. Ney
    Pages 137-180
  6. Krishna B. Athreya, Peter E. Ney
    Pages 181-228
  7. Krishna B. Athreya, Peter E. Ney
    Pages 229-267
  8. Back Matter
    Pages 268-290

About this book

Introduction

The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro­ cess, etc. We have tried to avoid the rather uneconomical and un­ enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.

Keywords

Branching process Galton-Watson process Martingale Poisson process Sharp Verzweigungsprozess branching random walk construction extinction probability probability proof random walk renewal theory techniques time

Authors and affiliations

  • Krishna B. Athreya
    • 1
  • Peter E. Ney
    • 1
  1. 1.University of WisconsinMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65371-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-65373-5
  • Online ISBN 978-3-642-65371-1
  • Series Print ISSN 0072-7830
  • About this book