Measure-Valued Branching Markov Processes
Measure-Valued Branching Markov Processes
复制标题
DOI：
10.1007/978-3-642-15004-3
复制
发表时间：
2010-12
期刊：
影响因子：
--
通讯作者：
Zenghu Li
中科院分区：
文献类型：
--
作者：
Zenghu Li
一个测度值过程描述了一个种群的进化，它是按照机会法则进化的。在这一章中，我们给出了测度值分支过程的一些基本刻画和构造。特别地，我们建立了这些过程和累积量半群之间的一一对应关系。证明了非线性积分发展方程的一些结果，从而得到了一类测度值分支过程的解析构造，即所谓的Dawson-Watanabe超过程.我们将构造超过程的容许杀伤密度和一般的分支机制，不一定分解成本地和非本地的部分。给出了超过程的矩公式。
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.