Header

UZH-Logo

Maintenance Infos

Stochastic flows associated to coalescent processes


Bertoin, Jean; Le Gall, J-F (2003). Stochastic flows associated to coalescent processes. Probability Theory and Related Fields, 126(2):261-288.

Abstract

We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Möhle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size. We define a bridge to be a right-continuous process (B(r),r ∈ [0,1]) with nondecreasing paths and exchangeable increments, such that B(0)=0 and B(1)=1. We show that flows of bridges are in one-to-one correspondence with the so-called exchangeable coalescents. This yields an infinite-dimensional version of the classical Kingman representation for exchangeable partitions of ℕ. We then propose a Poissonian construction of a general class of flows of bridges and identify the associated coalescents. We also discuss an important auxiliary measure-valued process, which is closely related to the genealogical structure coded by the coalescent and can be viewed as a generalized Fleming-Viot process.

Abstract

We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Möhle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size. We define a bridge to be a right-continuous process (B(r),r ∈ [0,1]) with nondecreasing paths and exchangeable increments, such that B(0)=0 and B(1)=1. We show that flows of bridges are in one-to-one correspondence with the so-called exchangeable coalescents. This yields an infinite-dimensional version of the classical Kingman representation for exchangeable partitions of ℕ. We then propose a Poissonian construction of a general class of flows of bridges and identify the associated coalescents. We also discuss an important auxiliary measure-valued process, which is closely related to the genealogical structure coded by the coalescent and can be viewed as a generalized Fleming-Viot process.

Statistics

Citations

59 citations in Web of Science®
53 citations in Scopus®
Google Scholar™

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Flow – Coalescence – Exchangeability – Bridge
Language:English
Date:2003
Deposited On:03 Jul 2013 13:17
Last Modified:05 Apr 2016 16:51
Publisher:Springer
ISSN:0178-8051
Publisher DOI:https://doi.org/10.1007/s00440-003-0264-4
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1990057
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1023.92018

Download

Full text not available from this repository.
View at publisher