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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.

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:05 Apr 2016 16:49
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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