Related papers: Some smooth divergences for $\ell_{1}-$approximati…
We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO…
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.
We classify deformation quantizations of the symplectic supervarieties that are smooth and admissible. This generalizes the corresponding result of Bezrukavnikov and Kaledin to the super case. We relate the equivalence classes of…
Estimating divergences in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential…
The Kolmogorov distances between a symmetric hypergeometric law with standard deviation $\sigma$ and its usual normal approximations are computed and shown to be less than $1/(\sqrt{8\pi}\,\sigma)$, with the order $1/\sigma$ and the…
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in any cylindrical smooth domain with smooth boundary data one can find an approximating equation…
We report closed-form formula for calculating the Chi square and higher-order Chi distances between statistical distributions belonging to the same exponential family with affine natural space, and instantiate those formula for the Poisson…
Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative…
Under correlation-type conditions, we derive an upper bound of order $(\log n)/n$ for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved…
We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
We present some new examples of separable (\mathcal_\infty) spaces which are (\ell_r) saturated for some (1 < r < \infty).
In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.
We aim at giving a rigorous proof of the state-ments on the smoothness and the dimension of Severi varieties wherethere are gaps in the proofs in some standard literature. The method isa mixture of algebraic and analytic methods.
It is natural to expect the following loosely stated approximation principle to hold: a numerical approximation solution should be in some sense as smooth as its target exact solution in order to have optimal convergence. For piecewise…
For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…
Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…