Stochastic Evolution of genealogies of spatial populations: state description, characterization of dynamics and properties

Depperschmidt A, Greven A (2018)

Publication Language: English

Publication Type: Journal article, Online publication

Publication year: 2018

Journal

arXiv arXiv.org

DOI: 10.1142/9789811206092_0002

Open Access Link: http://arxiv.org/abs/1807.03637

Abstract

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.

Authors with CRIS profile

Andrej Depperschmidt Lehrstuhl für Mathematische Stochastik Andreas Greven Lehrstuhl für Mathematische Stochastik

How to cite

APA:

Depperschmidt, A., & Greven, A. (2018). Stochastic Evolution of genealogies of spatial populations: state description, characterization of dynamics and properties. arXiv. https://dx.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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