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

Beitrag in einer Fachzeitschrift
(Online-Publikation)


Details zur Publikation

Autorinnen und Autoren: Depperschmidt A, Greven A
Zeitschrift: arXiv
Jahr der Veröffentlichung: 2018
ISSN: 2331-8442
Sprache: Englisch


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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Depperschmidt, Andrej Dr.
Lehrstuhl für Mathematische Stochastik
Greven, Andreas Prof. Dr.
Lehrstuhl für Mathematische Stochastik


Zitierweisen

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

MLA:
Depperschmidt, Andrej, and Andreas Greven. "Stochastic Evolution of genealogies of spatial populations: state description, characterization of dynamics and properties." arXiv (2018).

BibTeX: 

Zuletzt aktualisiert 2018-17-07 um 09:53