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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 24 open journal systems 


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

Sergey V. Lototsky, University of Southern California


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 $bR^d$ 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.


Full text: PDF

Pages: 1-14

Published on: October 17, 2001


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Electronic Journal of Probability. ISSN: 1083-6489