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Collision Local Times, Historical Stochastic Calculus, and Competing Species

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Collision Local Times, Historical Stochastic Calculus, and Competing Species
2.	Creator	Author's name, affiliation, country	Steven N. Evans; University of California at Berkeley
2.	Creator	Author's name, affiliation, country	Edwin A. Perkins; The University of British Columbia
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	super-process, super-Brownian motion, interaction, local time, historical process, measure-valued Markov branching process, stochastic calculus, martingale measure, random measure
3.	Subject	Subject classification	60K35, 60J55, 60H99, 60G57
4.	Description	Abstract	Branching measure-valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified by a competitive interaction mechanism under which individuals from each population have their longevity or fertility adversely affected by collisions with individuals from the other population. For 3 or fewer spatial dimensions, such processes are constructed using a new fixed-point technique as the unique solution of a strong equation driven by another pair of more explicitly constructible measure-valued diffusions. This existence and uniqueness is used to establish well-posedness of the related martingale problem and hence the strong Markov property for solutions. Previous work of the authors has shown that in 4 or more dimensions models with the analogous definition do not exist.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1998-04-08
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/27
10.	Identifier	Digital Object Identifier	10.1214/EJP.v3-27
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 3
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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