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Titlebook: Measure-Valued Branching Markov Processes; Zenghu Li Textbook 20111st edition Springer-Verlag Berlin Heidelberg 2011 60J80; 60G57; 60J70;

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Random Measures on Metric Spaces,lued processes. In particular, we give some characterizations of the convergence of random measures in terms of their Laplace functionals. Based on these results, a general representation for the distributions of infinitely divisible random measures is established. We also give some characterization
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One-Dimensional Branching Processes,cess with immigration which deals with the situation where immigrants may come from outer sources. In this chapter, we first give some characterizations of the extinction probabilities and evolution rates of CB-processes. Then we prove some conditional limit theorems for the processes that extinguis
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Branching Particle Systems,egions, families of neutrons in nuclear reactions, cosmic-ray showers and so on. In this chapter, we show that suitable scaling limits of those particle systems lead to the Dawson–Watanabe superprocesses in finite-dimensional distributions, giving intuitive interpretations for the superprocesses. To
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Martingale Problems of Superprocesses,th Dawson–Watanabe superprocesses. In particular, we shall prove the equivalence of a number of martingale problems for the superprocesses. The martingale problems induce martingale measures which are not necessarily orthogonal, but still worthy in the sense of Walsh (1986). We give a representation
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Structures of Independent Immigration,volution semigroups. Those semigroups are in one-to-one correspondence with infinitely divisible probability entrance laws for the MB-processes. We shall see that an immigration superprocess has a Borel right realization if the corresponding skew convolution semigroup is determined by a closable inf
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