# From flows of Lambda-Fleming-Viot processes to lookdown processes via flows of partitions

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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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (55)
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https://hal.archives-ouvertes.fr/hal-00609435
Contributeur : Cyril Labbé <>
Soumis le : mardi 19 juillet 2011 - 09:44:50
Dernière modification le : mercredi 21 mars 2018 - 18:56:48

### Identifiants

• HAL Id : hal-00609435, version 1
• ARXIV : 1107.3419

### Citation

Cyril Labbé. From flows of Lambda-Fleming-Viot processes to lookdown processes via flows of partitions. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (55). 〈hal-00609435〉

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