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Stability of the stochastic heat equation in $L^1([0,1])$


 
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1. Title Title of document Stability of the stochastic heat equation in $L^1([0,1])$
 
2. Creator Author's name, affiliation, country Nicolas Fournier; Université Paris Est
 
2. Creator Author's name, affiliation, country Jacques Printems; Université Paris Est
 
3. Subject Discipline(s)
 
3. Subject Keyword(s)
 
4. Description Abstract We consider the white-noise driven stochastic heat equation on $[0,1]$ with Lipschitz-continuous drift and diffusion coefficients. We derive an inequality for the $L^1([0,1])$-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some estimates which allow us to study the stability of the solution with respect the initial condition, the uniqueness of the possible invariant distribution and the asymptotic confluence of solutions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-05-30
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1636
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1636
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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