Branching Processes

1. Front Matter

   Pages i-x

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2. Introduction

   1. Branching Phenomena and Models

      • Søren Asmussen, Heinrich Hering

      Pages 1-16

3. Simple Branching Processes

   1. The Galton-Watson Process: Probabilistic Methods

      • Søren Asmussen, Heinrich Hering

      Pages 17-54

   2. The Galton-Watson Process: Analytic Methods

      • Søren Asmussen, Heinrich Hering

      Pages 55-113

   3. Continuous Time Markov Branching Processes

      • Søren Asmussen, Heinrich Hering

      Pages 115-136

4. Multigroup Branching Diffusions on Bounded Domains

   1. Foundations

      • Søren Asmussen, Heinrich Hering

      Pages 137-182

   2. Limit Theory for Subcritical and Critical Processes

      • Søren Asmussen, Heinrich Hering

      Pages 183-240

   3. Basic Limit Theory for Supercritical Processes

      • Søren Asmussen, Heinrich Hering

      Pages 241-288

   4. More on the Limiting Behaviour of Linear Functionals

      • Søren Asmussen, Heinrich Hering

      Pages 289-346

5. Related Models

   1. Unbounded Domains

      • Søren Asmussen, Heinrich Hering

      Pages 347-359

   2. Generalized Age-Dependence and Random Characteristics

      • Søren Asmussen, Heinrich Hering

      Pages 361-402

   3. Two-Sex Models

      • Søren Asmussen, Heinrich Hering

      Pages 403-427

6. Back Matter

   Pages 429-461

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Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat­ ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo­ nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre­ sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.

• Branching process
• Galton-Watson process
• Law of large numbers
• Martingale
• Maxima
• Uniform integrability

• Institute of Mathematical Stochastik, University of Copenhagen, Copenhagen ø, Denmark

  Søren Asmussen

• Institut für Mathematische Statistik, Universität Göttingen, Göttingen, West Germany

  Heinrich Hering

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