Stochastic Evolution of Genealogies of Spatial Populations: State Description, Characterization of Dynamics and Properties
Stochastic Evolution of Genealogies of Spatial Populations: State Description, Characterization of Dynamics and Properties
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DOI：
10.1142/9789811206092_0002
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
A. Depperschmidt;A. Greven
中科院分区：
文献类型：
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作者：
A. Depperschmidt;A. Greven
本文综述了在(有标记的)超度量空间上用树值马尔可夫过程刻画种群的随机演化谱系和多类型种群或空间种群的标记谱系的结果。特别地，我们解释了状态空间及其拓扑的选择，用适定的鞅问题描述了谱系Fleming-Viot模型和分枝模型的动力学，并给出了关于长期行为的典型结果。此外，我们还讨论了作为分析对偶的不同形式和Girsanov变换的两个关键工具的证明和草图的基本技巧。
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In particular we explain the choice of state spaces and their topologies, describe the dynamics of genealogical Fleming-Viot and branching models by well-posed martingale problems, and formulate the typical results on the longtime behavior. Furthermore we discuss the basic techniques of proofs and sketch as two key tools of analysis the different forms of duality and the Girsanov transformation.