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Competing Species Superprocesses with Infinite Variance

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Competing Species Superprocesses with Infinite Variance
2.	Creator	Author's name, affiliation, country	Klaus Fleischmann; Weierstrass Institute for Applied Analysis and Stochastics
2.	Creator	Author's name, affiliation, country	Leonid Mytnik; Technion - Israel Institute of Technology
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Superprocess with killing, competing superprocesses, interactive superprocesses, superprocess with immigration, measure-valued branching, interactive branching, state-dependent branching, collision measure, collision local time, martingale problem.
3.	Subject	Subject classification	Primary 60K35; Secondary 60G57, 60J80
4.	Description	Abstract	We study pairs of interacting measure-valued branching processes (superprocesses) with alpha-stable migration and $(1+\beta)$-branching mechanism. The interaction is realized via some killing procedure. The collision local time for such processes is constructed as a limit of approximating collision local times. For certain dimensions this convergence holds uniformly over all pairs of such interacting superprocesses. We use this uniformity to prove existence of a solution to a competing species martingale problem under a natural dimension restriction. The competing species model describes the evolution of two populations where individuals of different types may kill each other if they collide. In the case of Brownian migration and finite variance branching, the model was introduced by Evans and Perkins (1994). The fact that now the branching mechanism does not have finite variance requires the development of new methods for handling the collision local time which we believe are of some independent interest.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	German Science Foundation, Israel Science Foundation
7.	Date	(YYYY-MM-DD)	2003-05-22
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/136
10.	Identifier	Digital Object Identifier	10.1214/EJP.v8-136
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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