Measure-valued branching Markov processes / Zenghu Li

The present book is written for the purpose of providing a compact and rigorous basic theory of measure-valued branching processes and immigration processes. Roughly speaking, this book is divided into two parts. The first part consists of Chapters 1–7, which treat the analytic construction of Dawson-Watanabe superprocesses with general branching mechanisms, regularities of superprocesses, unified treatment of different models, and martingale problems of superprocesses. A point worthy to note is the adoption of a general setting like Borel right processes in a Lusin topological space E as the underlying spatial motions. The second part consists of Chapters 8–12, which treat mainly the immigration structures associated with measure-valued branching processes. A peculiar feature here is the usage of skew convolution semigroups in an axiomatic definition of immigration processes. The skew convolution semigroups associated with a given measure-valued branching process are in one-to-one correspondence with its infinitely divisible probability entrance laws, and the immigration superprocess has regularity similar to that of the Dawson-Watanabe superprocess if the corresponding probability entrance law is closable. ... (Zentralblatt)

Bibliogr. p. 333-344. Index