Measure-Valued Branching Processes (original) (raw)

Abstract

A measure-valued process describes the evolution of a population that evolves according to the law of chance. In this chapter we provide some basic characterizations and constructions for measure-valued branching processes. In particular, we establish a one-to-one correspondence between those processes and cumulant semigroups. Some results for nonlinear integral evolution equations are proved, which lead to an analytic construction of a class of measure-valued branching processes, the so-called Dawson–Watanabe superprocesses. We shall construct the superprocesses for admissible killing densities and general branching mechanisms that are not necessarily decomposable into local and non-local parts. A number of moment formulas for the superprocesses are also given.

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  1. School of Mathematical Sciences, Beijing Normal University, No. 19 Xinjie Kouwai Street, Haidian District, Beijing, 100875, People’s Republic of China
    Zenghu Li

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  1. Zenghu Li
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© 2011 Springer-Verlag Berlin Heidelberg

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Li, Z. (2011). Measure-Valued Branching Processes. In: Measure-Valued Branching Markov Processes. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15004-3\_2

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