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Li, Zenghu

Measure-Valued Branching Markov Processes (Gebundene Ausgabe)

Reihe: Probability and its Applications

Springer-Verlag GmbH, Springer Berlin, November 2010

Edition - 350 S. - Sprache: Englisch - Bibliographie - 243x167x30 mm Book

ISBN: 3642150039 EAN: 9783642150036

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.

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For the first time a book in this research areaGives treatments of the basic regularities of Dawson-Watanabe superprocesses with general branching mechanisms and spatial motionsStudies immigration superprocesses and generalized Ornstein-Uhlenbeck processesDesigned as a study text for graduates


Preface.- 1. Random Measures on Metric Spaces.- 2. Measure-valued Branching Processes.- 3. One-dimensional Branching Processes.- 4. Branching Particle Systems.- 5. Basic Regularities of Superprocesses.- 6. Constructions by Transformations.- 7. Martingale Problems of Superprocesses.- 8. Entrance Laws and Excursion Laws.- 9. Structures of Independent Immigration.- 10. State-dependent Immigration Structures.- 11. Generalized Ornstein-Uhlenbeck Processes.- 12. Small Branching Fluctuation Limits.- 13. Appendix: Markov Processes.- Bibliography.- Index.


From the 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)

ISBN 3-642-15003-9

ISBN 978-3-642-15003-6

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