A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks

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dc.creatorBirkner, Matthias
dc.creatorBlath, Jochen
dc.creatorMoehle, Martin
dc.creatorSteinruecken, Matthias
dc.creatorTams, Johanna
dc.date2008-08-04
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:12:55Z
dc.date.available2026-07-07T10:12:55Z
dc.descriptionLet $Λ$ be a finite measure on the unit interval. A $Λ$-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions ($Λ$-coalescent) in analogy to the duality known for the classical Fleming Viot process and Kingman's coalescent, where $Λ$ is the Dirac measure in 0. We explicitly construct a dual process of the coalescent with simultaneous multiple collisions ($Ξ$-coalescent) with mutation, the $Ξ$-Fleming-Viot process with mutation, and provide a representation based on the empirical measure of an exchangeable particle system along the lines of Donnelly and Kurtz (1999). We establish pathwise convergence of the approximating systems to the limiting $Ξ$-Fleming-Viot process with mutation. An alternative construction of the semigroup based on the Hille-Yosida theorem is provided and various types of duality of the processes are discussed. In the last part of the paper a population is considered which undergoes recurrent bottlenecks. In this scenario, non-trivial $Ξ$-Fleming-Viot processes naturally arise as limiting models.
dc.description35 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0808.0412
dc.identifierhttp://arxiv.org/abs/0808.0412
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172352
dc.subjectProbability
dc.subject60K35, 60G09, 92D10 (Primary) 60C05, 92D15 (Secondary)
dc.titleA modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks
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