Zenghu Li

Measure-Valued Branching Markov Processes (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 350
• Erscheinungstermin: 10. November 2010
• Englisch
• ISBN-13: 9783642150043
• Artikelnr.: 44226261

Autorenporträt

Zenghu Li is a Changjiang Scholar Distinguished Professor at Beijing Normal University and a Fellow of the Institute of Mathematical Statistics. He serves on the editorial board for several mathematical journals and book series, including Acta Mathematica Sinica and Stochastic Processes and Their Applications. His research interests include branching Markov processes, measure-valued Markov processes, stochastic differential equations and applications.

Inhaltsangabe

Preface to the Second Edition.- Preface to the First Edition.- Conventions and Notations.- 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 Kuznetsov Measures.- 9. Structures of Independent Immigration.- 10. One-Dimensional Stochastic Equations.- 11. Path-Valued Processes and Stochastic Flows.- 12. State-Dependent Immigration Structures.- 13. Generalized Ornstein-Uhlenbeck Processes.- 14. Small-Branching Fluctuation Limits.- A. Markov Processes.- References.- Subject Index.- Symbol Index.

Rezensionen

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)