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New results on pathwise uniqueness for the heat equation with colored noise


 
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1. Title Title of document New results on pathwise uniqueness for the heat equation with colored noise
 
2. Creator Author's name, affiliation, country Thomas Rippl; University of Goettingen; Germany
 
2. Creator Author's name, affiliation, country Anja Sturm; University of Goettingen; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Heat equation, colored noise, stochastic partial differential equation, pathwise uniqueness, existence
 
3. Subject Subject classification 60H15; 60K35; 60K37; 60J80
 
4. Description Abstract We consider strong uniqueness and thus also existence of strong solutions for the stochastic heat equation with  a multiplicative colored noise term. Here, the noise is white in time and colored in $q$ dimensional space ($q \geq 1$) with a singular correlation kernel. The noise coefficient is Hölder continuous in the solution. We discuss improvements of the sufficient conditions obtained in Mytnik, Perkins and Sturm (2006) that relate the Hölder coefficient with the singularity of the correlation kernel of the noise. For this we use new ideas of Mytnik and Perkins (2011) who treat the case of strong uniqueness for the stochastic heat equation with multiplicative white noise in one dimension. Our main result on pathwise uniqueness confirms a conjecture that was put forward in their paper.
 
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7. Date (YYYY-MM-DD) 2013-08-24
 
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/2506
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2506
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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