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 andgeneral branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularityof 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 studentsin probability theory and stochastic processes. 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 INDICE: 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 byTransformations.- 7. Martingale Problems of Superprocesses.- 8. Entrance Lawsand 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.
- ISBN: 978-3-642-15003-6
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 350
- Fecha Publicación: 01/11/2010
- Nº Volúmenes: 1
- Idioma: Inglés