On divergence form SPDEs with VMO coefficients in a half space
نویسندگان
چکیده
منابع مشابه
On Divergence Form SPDEs with VMO Coefficients
We present several results on solvability in Sobolev spaces W 1 p of SPDEs in divergence form in the whole space.
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We extend several known results on solvability in the Sobolev spaces W 1 p , p ∈ [2,∞), of SPDEs in divergence form in R d + to equations having coefficients which are discontinuous in the space variable.
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We present several results on the smoothness in Lp sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form filtering equation which are usually considered in terms of formally adjoint to operators in nondivergence form.
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We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the second power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variable.
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Equations of the form du = (auxixj +Dif i) dt+ ∑ k (σuxi + g k) dwk t are considered for t > 0 and x ∈ R+. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power p ∈ [2,∞).
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2009
ISSN: 0304-4149
DOI: 10.1016/j.spa.2008.11.003