Probability and Its Applications

Measure-Valued Branching Markov Processes

Authors: Li, Zenghu

  • For the first time a book in this research area
  • Gives treatments of the basic regularities of Dawson-Watanabe superprocesses with general branching mechanisms and spatial motions
  • Studies immigration superprocesses and generalized Ornstein-Uhlenbeck processes
  • Designed as a study text for graduates
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  • ISBN 978-3-642-15004-3
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Hardcover $74.95
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  • ISBN 978-3-642-15003-6
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Softcover $74.95
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  • ISBN 978-3-642-26620-1
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Rent the ebook  
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About this Textbook

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.

Reviews

From the book reviews:

“The present book appears to be the first monograph in textbook format that provides a rigorous treatment of general theory for a wide class of measure-valued processes. … A selection of good examples throughout the book helps clarify the results. … This is a well-written, concise and dedicated book. It will serve excellently as a platform and reference for the next phase of development of superprocesses and measure-valued branching processes.” (Ingemar Kaj, Mathematical Reviews, Issue 2012 c)

“The present book is written for the purpose of providing a compact and rigorous basic theory of measured-valued branching processes and immigration processes. … this book is well organized, the presentation is very systematic and sufficiently simple, and the key points are easy to understand. … It is recommendable for graduate students and researchers working in the field of measure-valued processes and their related topics, including stochastic processes and probability theory.” (Isamu Dôku, Zentralblatt MATH, Vol. 1235, 2012)

“The main purpose of this book is to give a compact and rigorous treatment of the basic theory of measure-valued branching processes and immigration processes. … This book can be used as a reference of the basics of Dawson–Watanabe superprocesses and immigration superprocesses. It can also be used in a course for graduate students specialized in probability and stochastic processes.” (Gyula Pap, Acta Scientiarum Mathematicarum (Szeged), Vol. 77 (3-4), 2011)


Table of contents (12 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-15004-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-3-642-15003-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-3-642-26620-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Measure-Valued Branching Markov Processes
Authors
Series Title
Probability and Its Applications
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-15004-3
DOI
10.1007/978-3-642-15004-3
Hardcover ISBN
978-3-642-15003-6
Softcover ISBN
978-3-642-26620-1
Series ISSN
1431-7028
Edition Number
1
Number of Pages
XI, 350
Topics