Measure-Valued Branching Markov Processes

Probability and its Applications
Aus der Reihe: Probability and its Applications

Li, Zenghu

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Springer-Verlag GmbH; Springer Berlin , November 2010
350 S. - Sprache: eng - Bibliographie - 243x167x30 mm
Wahrscheinlichkeitstheorie ( Wahrscheinlichkeit ), Wahrscheinlichkeit - Wahrscheinlichkeitstheorie, Mathematik / Statistik, Stochastik, Wahrscheinlichkeitsrechnung, Wahrscheinlichkeitsrechnung und Statistik
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.
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.

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