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2014 From flows of $\Lambda$-Fleming-Viot processes to lookdown processes via flows of partitions
Cyril Labbé
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Electron. J. Probab. 19: 1-49 (2014). DOI: 10.1214/EJP.v19-3192

Abstract

The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $\Lambda$-Fleming-Viot process along with its genealogy. First we introduce the stochastic flow of partitions and show that it provides a new formulation of the lookdown representation. Second we study the asymptotic behaviour of the $\Lambda$-Fleming-Viot process and we provide sufficient conditions for the existence of an infinite sequence of Eves that generalise the primitive Eve of Bertoin and Le Gall. Finally under the condition that this infinite sequence of Eves does exist, we construct the lookdown representation pathwise from a flow of bridges.

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Cyril Labbé. "From flows of $\Lambda$-Fleming-Viot processes to lookdown processes via flows of partitions." Electron. J. Probab. 19 1 - 49, 2014. https://doi.org/10.1214/EJP.v19-3192

Information

Accepted: 25 June 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1334.60152
MathSciNet: MR3227064
Digital Object Identifier: 10.1214/EJP.v19-3192

Subjects:
Primary: 60J25
Secondary: 60G09 , 92D25

Keywords: Coalescent , Exchangeable bridge , Fleming-Viot process , Lookdown process , Partition , stochastic flow

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