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Extending the Martingale Measure Stochastic Integral With Applications to Spatially Homogeneous S.P.D.E.'s

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Extending the Martingale Measure Stochastic Integral With Applications to Spatially Homogeneous S.P.D.E.'s
2.	Creator	Author's name, affiliation, country	Robert C. Dalang; Ecole Polytechnique Fédérale
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	stochastic wave equation, stochastic heat equation,Gaussian noise, process solution.
3.	Subject	Subject classification	Primary 60H15; Secondary 60H05, 35R60, 35D10.
4.	Description	Abstract	We extend the definition of Walsh's martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green's function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even when the integrand is a distribution, the value of our stochastic integral process is a real-valued martingale. We use this extended integral to recover necessary and sufficient conditions under which the linear wave equation driven by spatially homogeneous Gaussian noise has a process solution, and this in any spatial dimension. Under this condition, the non-linear three dimensional wave equation has a global solution. The same methods apply to the damped wave equation, to the heat equation and to various parabolic equations.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-03-24
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/43
10.	Identifier	Digital Object Identifier	10.1214/EJP.v4-43
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 4
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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