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


Bertoin, Jean; Le Gall, J-F (2005). Stochastic flows associated to coalescent processes. II: Stochastic differential equations. Annales de l'Institut Henri Poincaré (B) Probabilities et Statistiques, 41(3):307-333.

Abstract

We obtain precise information about the stochastic flows of bridges that are associated with the so-called Λ-coalescents. When the measure Λ 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 Λ=δ0 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.

Abstract

We obtain precise information about the stochastic flows of bridges that are associated with the so-called Λ-coalescents. When the measure Λ 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 Λ=δ0 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.

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18 citations in Web of Science®
16 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:19 Jun 2013 13:14
Last Modified:07 Dec 2017 21:24
Publisher:Elsevier
ISSN:0246-0203
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.anihpb.2004.07.003
Related URLs:http://www.numdam.org/item?id=AIHPB_2005__41_3_307_0 (Organisation)

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