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On Convergence of Population Processes in Random Environments to the Stochastic Heat Equation with Colored Noise

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On Convergence of Population Processes in Random Environments to the Stochastic Heat Equation with Colored Noise
2.	Creator	Author's name, affiliation, country	Anja Sturm; Technische Universität Berlin
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Heat equation, colored noise, stochastic partial differential equation, superprocess, weak convergence, particle representation, random environment, existence theorem
3.	Subject	Subject classification	60H15, 60K35, 60K37, 60J80, 60F05
4.	Description	Abstract	We consider the stochastic heat equation with a multiplicative colored noise term on the real space for dimensions greater or equal to 1. First, we prove convergence of a branching particle system in a random environment to this stochastic heat equation with linear noise coefficients. For this stochastic partial differential equation with more general non-Lipschitz noise coefficients we show convergence of associated lattice systems, which are infinite dimensional stochastic differential equations with correlated noise terms, provided that uniqueness of the limit is known. In the course of the proof, we establish existence and uniqueness of solutions to the lattice systems, as well as a new existence result for solutions to the stochastic heat equation. The latter are shown to be jointly continuous in time and space under some mild additional assumptions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	The Rhodes Trust and DFG Priority Program 1033.
7.	Date	(YYYY-MM-DD)	2003-04-11
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/129
10.	Identifier	Digital Object Identifier	10.1214/EJP.v8-129
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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