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  • © 1972

Branching Processes

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

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  • ISBN: 978-3-642-65371-1
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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XI
  2. The Galton-Watson Process

    • Krishna B. Athreya, Peter E. Ney
    Pages 1-65
  3. Potential Theory

    • Krishna B. Athreya, Peter E. Ney
    Pages 66-101
  4. One Dimensional Continuous Time Markov Branching Processes

    • Krishna B. Athreya, Peter E. Ney
    Pages 102-136
  5. Age-Dependent Processes

    • Krishna B. Athreya, Peter E. Ney
    Pages 137-180
  6. Multi-Type Branching Processes

    • Krishna B. Athreya, Peter E. Ney
    Pages 181-228
  7. Special Processes

    • Krishna B. Athreya, Peter E. Ney
    Pages 229-267
  8. Back Matter

    Pages 268-290

About this book

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

  • University of Wisconsin, Madison, USA

    Krishna B. Athreya, Peter E. Ney

Bibliographic Information

  • Book Title: Branching Processes

  • Authors: Krishna B. Athreya, Peter E. Ney

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-65371-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • Softcover ISBN: 978-3-642-65373-5

  • eBook ISBN: 978-3-642-65371-1

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 288

  • Topics: Applications of Mathematics

Buying options

eBook
USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-65371-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 119.99
Price excludes VAT (USA)