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Nonlinear historical superprocess approximations for population models with past dependence

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Nonlinear historical superprocess approximations for population models with past dependence
2.	Creator	Author's name, affiliation, country	Sylvie Méléard; École Polytechnique; France
2.	Creator	Author's name, affiliation, country	Viet Chi Tran; Université des Sciences et Technologies de Lille; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Nonlinear historical superprocess; Genealogical interacting particle system; Limit theorem; Evolution models
3.	Subject	Subject classification	60J80; 60J68; 60K35
4.	Description	Abstract	We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend on the trait of the ancestors and on its past and allows interactions between individuals through their lineages. We define an interacting historical particle process  describing the  genealogies of the living individuals; it takes values in the space of point measures  on an infinite dimensional càdlàg path space. This individual-based process can be approximated by  a nonlinear historical superprocess, under the assumptions of large populations, small individuals and allometric demographies. Because of the interactions, the branching property fails and we use martingale problems and fine couplings between our population and independent branching particles. Our convergence theorem is illustrated by two examples of current interest in biology. The first one relates the biodiversity history of a population and its phylogeny, while the second treats a spatial model where individuals compete through their past trajectories.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR MANEGE (ANR-09-BLAN-0215); "Chaire Modélisation Mathématiques et Biodiversité" of Veolia Environnement-Ecole Polytechnique-Museum National d'Histoire Naturelle-Fondation X; Institute for Mathematical Sciences of the National University of Singapore
7.	Date	(YYYY-MM-DD)	2012-06-18
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/2093
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-2093
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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