Flots stochastiques et représentation lookdown
type: Dataset
description: This thesis focuses on mathematical properties of two population models, namely the generalised Fleming-Viot process and the branching process. In both cases, the population is composed of infinitely many individuals characterised by a genetic type. As time passes, the asymptotic frequencies of the types within the population evolve stochastically through reproduction events where a uniformly chosen individual gives birth to a progeny with the same genetic type. Mathematically these two models are defined by measure-valued processes. In order to give a meaning to the genealogy of the underlying population, several approaches have been proposed these last fifteen years. One of the main contributions of this thesis is to unify two constructions: the lookdown representation introduced by Peter Donnelly and Thomas Kurtz in 1999 and the stochastic flow of bridges (or subordinators) introduced by Jean Bertoin and Jean-François Le Gall in 2000. This unification relies on the definition of new objects (the Eves, the stochastic flow of partitions) and necessitates a fine study of the asymptotic behaviours of the two aforementioned population models. In particular we define the Eve property as follows: if there is a genetic type whose asymptotic frequency tends to $1$ as $t$ becomes large then the population asymptotically descends from a single ancestor called the Eve of the population. In the case of the branching process, we obtain a necessary and sufficient condition on the branching mechanism ensuring the Eve property. We also provide a complete classification of all the possible asymptotic behaviours according to the branching mechanism. In the case of the generalised Fleming-Viot process, we obtain a partial classification of the possible asymptotic behaviours. Finally when the Eve property is fulfilled we present a pathwise construction of the lookdown representation from a stochastic flow of bridges (or subordinators). We also present a complete study of the explosiv…
issued: 2026-05-09T07:59:01.336114
language: en
modified: 2026-05-09T07:59:01.336118
contact point: Organization
  fn: CCSD
keyword: coalescent
keyword: flot-stochastique
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lookdown
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: partition
keyword: pont-echangeable
keyword: processus-a-valeur-mesure
keyword: processus-de-branchement
keyword: theses
landing page: https://theses.hal.science/tel-00874551

Flots stochastiques et représentation lookdown
type: Distribution
format: HTML
issued: 2026-05-09T07:59:01.337583
modified: 2026-05-09T07:59:01.319677
access URL: https://theses.hal.science/tel-00874551

test_moissonnage_selune
type: Agent