Measure-Valued Branching Markov Processes

  • Zenghu Li

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

Table of contents

  1. Front Matter
    Pages I-XI
  2. Zenghu Li
    Pages 1-28
  3. Zenghu Li
    Pages 29-56
  4. Zenghu Li
    Pages 57-85
  5. Zenghu Li
    Pages 87-105
  6. Zenghu Li
    Pages 107-125
  7. Zenghu Li
    Pages 127-144
  8. Zenghu Li
    Pages 145-178
  9. Zenghu Li
    Pages 179-206
  10. Zenghu Li
    Pages 207-232
  11. Zenghu Li
    Pages 233-253
  12. Zenghu Li
    Pages 281-299
  13. Back Matter
    Pages 301-350

About this book

Introduction

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups.

The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Keywords

60J80; 60G57; 60J70; 60J85; 60J35; 60J40 Dawson-Watanabe superprocess entrance law generalized Ornstein-Uhlenbeck process immigration superprocess skew convolution semigroup

Authors and affiliations

  • Zenghu Li
    • 1
  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina, People's Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-15004-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-15003-6
  • Online ISBN 978-3-642-15004-3
  • Series Print ISSN 1431-7028
  • About this book