Depperschmidt A, Greven A (2018)
Publication Language: English
Publication Type: Journal article, Online publication
Publication year: 2018
DOI: 10.1142/9789811206092_0002
Open Access Link: http://arxiv.org/abs/1807.03637
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
behaviour. 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.
APA:
Depperschmidt, A., & Greven, A. (2018). Stochastic Evolution of genealogies of spatial populations: state description, characterization of dynamics and properties. arXiv. https://doi.org/10.1142/9789811206092_0002
MLA:
Depperschmidt, Andrej, and Andreas Greven. "Stochastic Evolution of genealogies of spatial populations: state description, characterization of dynamics and properties." arXiv (2018).
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