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Convergence of Rescaled Competing Species Processes to a Class of SPDEs

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1.	Title	Title of document	Convergence of Rescaled Competing Species Processes to a Class of SPDEs
2.	Creator	Author's name, affiliation, country	Sandra M Kliem; EURANDOM; Netherlands
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Voter model; Lotka-Volterra model; spatial competition; stochastic partial differential equations; long-range limits
3.	Subject	Subject classification	60F05; 60K35; 60H15
4.	Description	Abstract	One can construct a sequence of rescaled perturbations of voter processes in dimension $d=1$ whose approximate densities are tight. By combining both long-range models and fixed kernel models in the perturbations and considering the critical long-range case, results of Cox and Perkins (2005) are refined. As a special case we are able to consider rescaled Lotka-Volterra models with long-range dispersal and short-range competition. In the case of long-range interactions only, the approximate densities converge to continuous space time densities which solve a class of SPDEs (stochastic partial differential equations), namely the heat equation with a class of drifts, driven by Fisher-Wright noise. If the initial condition of the limiting SPDE is integrable, weak uniqueness of the limits follows. The results obtained extend the results of Mueller and Tribe (1995) for the voter model by including perturbations. In particular, spatial versions of the Lotka-Volterra model as introduced in Neuhauser and Pacala (1999) are covered for parameters approaching one. Their model incorporates a fecundity parameter and models both intra- and interspecific competition.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	The work of the author was supported by a ``St John's College Sir Quo-Wei Lee Fellowship'', a ``University of BC Graduate Fellowship'' and an NSERC Discovery Grant
7.	Date	(YYYY-MM-DD)	2011-03-29
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/870
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-870
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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