arXiv subjects

Cyril Labbé

Publications and source records attributed to Cyril Labbé.

39 records · Page 3Linked to original sources

arXiv2014

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

The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $Λ$-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 $Λ$-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.

math.PR↗

arXiv2014

On the Eve property for CSBP

We consider the population model associated to continuous state branching processes and we are interested in the so-called Eve property that asserts the existence of an ancestor with an overwhelming progeny at large times, and more generally, in the possible behaviours of the frequencies among the population at large times. In this paper, we classify all the possible behaviours according to the branching mechanism of the continuous state branching process.

math.PR↗

arXiv2013

Quasi-stationary distributions associated with explosive CSBP

We characterise all the quasi-stationary distributions and the Q-process associated with a continuous state branching process that explodes in finite time. We also provide a rescaling for the continuous state branching process conditioned on non-explosion when the branching mechanism is regularly varying at 0.

math.PR↗