
Homogenization of the LandauLifshitz equation
In this paper, we consider homogenization of the LandauLifshitz equatio...
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Stein kernels and moment maps
We describe a construction of Stein kernels using moment maps, which are...
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Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem
Consider the multivariate Stein equation Δ f  x·∇ f = h(x)  E h(Z), wh...
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Temporal semidiscretizations of a backward semilinear stochastic evolution equation
This paper studies the convergence of three temporal semidiscretization...
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Convergence of Lasserre's hierarchy: the general case
Lasserre's momentSOS hierarchy consists of approximating instances of t...
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Computational identification of the lowest spacewise dependent coefficient of a parabolic equation
In the present work, we consider a nonlinear inverse problem of identify...
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Formal Power Series on Algebraic Cryptanalysis
In cryptography, attacks that utilize a Gröbner basis have broken severa...
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Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem
We study the Darcy boundary value problem with lognormal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solution of the PDE by the expected value of its Taylor polynomial. The recursive deterministic equation satisfied by the expected value of the Taylor polynomial (first moment equation) is formally derived. Wellposedness and regularity results for the recursion are proved to hold in Sobolev spacevalued Hölder spaces with mixed regularity. The recursive first moment equation is then discretized by means of a sparse approximation technique, and the convergence rates are derived.
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