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Zbl 1119.60024
Bertoin, Jean; Le Gall, Jean-François
Stochastic flows associated to coalescent processes. II: Stochastic differential equations. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 41, No. 3, 307-333 (2005). ISSN 0246-0203

For part I see the authors [Probab. Theory Relat. Fields 126, No. 2, 261--288 (2003; Zbl 1023.92018)]. \par Summary: 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.

MSC 2000:: *60G09 Exchangeability
60J25 Markov processes with continuous parameter
60H20 Stochastic integral equations
92D15 Problems related to evolution

Keywords: Flow; Coalescence; Bridge; Stochastic differential equation

Citations: Zbl 1023.92018

Cited in: Zbl 1254.60088 Zbl 1110.60026

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