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Linear Stochastic Parabolic Equations, Degenerating on the Boundary of a Domain


 
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1. Title Title of document Linear Stochastic Parabolic Equations, Degenerating on the Boundary of a Domain
 
2. Creator Author's name, affiliation, country Sergey V. Lototsky; University of Southern California
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) $L_p$ estimates, Weighted spaces, Nonlinear filtering
 
3. Subject Subject classification 60H15, 35R60
 
4. Description Abstract A class of linear degenerate second-order parabolic equations is considered in arbitrary domains. It is shown that these equations are solvable using special weighted Sobolev spaces in essentially the same way as the non-degenerate equations in $R^d$ are solved using the usual Sobolev spaces. The main advantages of this Sobolev-space approach are less restrictive conditions on the coefficients of the equation and near-optimal space-time regularity of the solution. Unlike previous works on degenerate equations, the results cover both classical and distribution solutions and allow the domain to be bounded or unbounded without any smoothness assumptions about the boundary. An application to nonlinear filtering of diffusion processes is discussed.
 
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7. Date (YYYY-MM-DD) 2001-10-17
 
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/97
 
10. Identifier Digital Object Identifier 10.1214/EJP.v6-97
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 6
 
12. Language English=en en
 
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