Stochastic flows associated to coalescent processes II: Stochastic differential equations

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. (c) 2005 Elsevier SAS. All rights reserved.