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Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise


 
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1. Title Title of document Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise
 
2. Creator Author's name, affiliation, country David Marquez-Carreras; Universitat de Barcelona
 
2. Creator Author's name, affiliation, country Monica Sarra; Universitat de Barcelona
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic partial differential equation, stochastic heat equation, Gaussian noise, large deviation principle
 
3. Subject Subject classification 60H07, 60H15, 35R60
 
4. Description Abstract In this paper we prove a large deviation principle (LDP) for a perturbed stochastic heat equation defined on $[0,T]\times [0,1]^d$. This equation is driven by a Gaussian noise, white in time and correlated in space. Firstly, we show the Holder continuity for the solution of the stochastic heat equation. Secondly, we check that our Gaussian process satisfies an LDP and some requirements on the skeleton of the solution. Finally, we prove the called Freidlin-Wentzell inequality. In order to obtain all these results we need precise estimates of the fundamental solution of this equation.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2003-07-18
 
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/146
 
10. Identifier Digital Object Identifier 10.1214/EJP.v8-146
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 8
 
12. Language English=en
 
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