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Interacting diffusions and trees of excursions: convergence and comparison

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Interacting diffusions and trees of excursions: convergence and comparison
2.	Creator	Author's name, affiliation, country	Martin Hutzenthaler; University of Munich; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Island model; virgin island model; mean field model; McKean-Vlasov limit; extinction; excursion measure; many-demes-limit; propagation of chaos
3.	Subject	Subject classification	60K35; 60E15; 92D25
4.	Description	Abstract	We consider systems of interacting diffusions with local population regulation representing populations on countably many islands. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and diffusion coefficients. As a corollary, this entails a sufficient, explicit condition for extinction of the total mass as time tends to infinity. On the way to our comparison result, we establish that systems of interacting diffusions with uniform migration between finitely many islands converge to a tree of excursions as the number of islands tends to infinity. In the special case of logistic branching, this leads to a duality between a tree of excursions and the solution of a McKean-Vlasov equation.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2012-08-28
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2278
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-2278
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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