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Linear Stochastic Parabolic Equations, Degenerating on the Boundary of a Domain
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Sergey V. Lototsky, University of Southern California
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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.
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Full text: PDF
Pages: 1-14
Published on: October 17, 2001
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Electronic Journal of Probability. ISSN: 1083-6489 |
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