Tree-valued resampling dynamics martingale problems and applications

DOI10.1007/s00440-012-0413-8zbMath1379.60099arXiv0806.2224OpenAlexW2053533569MaRDI QIDQ1950379

Anita Winter, Peter Pfaffelhuber, Andreas Greven

Publication date: 13 May 2013

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.2224

zbMATH Keywords

dualityFleming-Viot processmartingale problemMoran modelgenealogical treetree-valued Markov processGromov-weak topology(ultra-)metric measure space

Mathematics Subject Classification ID

Problems related to evolution (92D15) Continuous-time Markov processes on general state spaces (60J25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (19)

The distribution of the spine of a Fleming-Viot type process ⋮ Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees) ⋮ Branching Processes -- A General Concept ⋮ Convergence of metric two-level measure spaces ⋮ Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property ⋮ Branching trees I: concatenation and infinite divisibility ⋮ Population dynamics and statistical physics in synergy. Abstracts from the workshop held March 6--12, 2022 ⋮ The Aldous chain on cladograms in the diffusion limit ⋮ The tree length of an evolving coalescent ⋮ Exchangeable coalescents, ultrametric spaces, nested interval-partitions: a unifying approach ⋮ A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes ⋮ Pathwise construction of tree-valued Fleming-Viot processes ⋮ The total external length of the evolving Kingman coalescent ⋮ Exchangeable hierarchies and mass-structure of weighted real trees ⋮ Evolving phylogenies of trait-dependent branching with mutation and competition. I: existence ⋮ The gap between Gromov-Vague and Gromov-Hausdorff-vague topology ⋮ Random systems in ultrametric spaces ⋮ Spaces of algebraic measure trees and triangulations of the circle ⋮ The evolving Moran genealogy

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