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A compact containment result for nonlinear historical superprocess approximations for population models with trait-dependence

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1.	Title	Title of document	A compact containment result for nonlinear historical superprocess approximations for population models with trait-dependence
2.	Creator	Author's name, affiliation, country	Sandra Kliem; Universitaet Duisburg-Essen; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	nonlinear historical superprocess, interacting particle systems, compact containment, tightness, exponential rates, evolution model, measure-valued processes on càdlàg functions, Polish space
3.	Subject	Subject classification	60J80 (Primary), 60G57, 60J68, 60K35 (Secondary)
4.	Description	Abstract	We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential times. Traits are hereditarily transmitted unless mutation occurs. The present model is an extension of the model used in [Méléard and Tran, EJP, 2012], where for large populations with small individual biomasses and under additional assumptions, the diffusive limit is shown to converge to a nonlinear historical superprocess. The main goal of the present article is to verify a compact containment condition in the more general setup of Polish trait-spaces and general mutation kernels that allow for a dependence on the parent's trait. As a by-product, a result on the paths of individuals is obtained. An application to evolving genealogies on marked metric measure spaces is mentioned where genealogical distance, counted in terms of the number of births without mutation, can be regarded as a trait. Because of the use of exponential times in the modeling of birth- and death-events the analysis of the modulus of continuity of the trait-history of a particle plays a major role in obtaining appropriate bounds.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	DFG through the SPP Priority Programme 1590
7.	Date	(YYYY-MM-DD)	2014-10-18
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/3506
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3506
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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