Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Stochastic flows associated to coalescent processes II : Stochastic differential equations

Auteur(s):

Code(s) de Classification MSC:

• 60G09 Exchangeability
• 60J25 Markov processes with continuous parameter
• 92D30 Epidemiology

Résumé: We obtain precise information about the stochastic flows of bridges that are associated with the so-called $\Lambda$-coalescents. When the measure $\Lambda$ gives no mass to $0$, we prove that the flow of bridges is generated by a stochastic differential equation driven by a Poisson point process. On the other hand, the case $\Lambda=\delta_0$ of the Kingman coalescent gives rise to a flow of coalescing diffusions on the interval $[0,1]$. We also discuss a remarkable Brownian flow on the circle which has close connections with the Kingman coalescent

Mots Clés: Flow ; coalescence ; bridge ; stochastic differential equation

Date: 2004-02-09

Prépublication numéro: PMA-881