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Weak Convergence for the Stochastic Heat Equation Driven by Gaussian White Noise

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Weak Convergence for the Stochastic Heat Equation Driven by Gaussian White Noise
2.	Creator	Author's name, affiliation, country	Xavier Bardina; Universitat Autònoma de Barcelona; Spain
2.	Creator	Author's name, affiliation, country	Maria Jolis; Universitat Autònoma de Barcelona; Spain
2.	Creator	Author's name, affiliation, country	Lluís Quer-Sardanyons; Universitat Autònoma de Barcelona; Spain
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	stochastic heat equation; white noise; weak convergence; two-parameter Poisson process; Donsker kernels
3.	Subject	Subject classification	60B12; 60G60; 60H15
4.	Description	Abstract	In this paper, we consider a quasi-linear stochastic heat equation with spatial dimension one, with Dirichlet boundary conditions and controlled by the space-time white noise. We formally replace the random perturbation by a family of noisy inputs depending on a parameter that approximate the white noise in some sense. Then, we provide sufficient conditions ensuring that the real-valued mild solution of the SPDE perturbed by this family of noises converges in law, in the space of continuous functions, to the solution of the white noise driven SPDE. Making use of a suitable continuous functional of the stochastic convolution term, we show that it suffices to tackle the linear problem. For this, we prove that the corresponding family of laws is tight and we identify the limit law by showing the convergence of the finite dimensional distributions. We have also considered two particular families of noises to that our result applies. The first one involves a Poisson process in the plane and has been motivated by a one-dimensional result of Stroock. The second one is constructed in terms of the kernels associated to the extension of Donsker's theorem to the plane.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Grant MTM2009-08869 from the Ministerio de Ciencia e Innovación
7.	Date	(YYYY-MM-DD)	2010-08-09
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/792
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-792
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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