Related papers: Density functions in high-dimensional basket optio…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks,…
Drawing on the theory of quantum mechanical stress, we introduce the stress density in density functional theory. In analogy with the Chetty-Martin energy density, the stress density provides a spatial resolution of the contributions to the…
The solutions of the Wigner-transformed time-dependent Hartree--Fock--Bogoliubov equations are studied in the constant-$\Delta$ approximation. This approximation is known to violate particle-number conservation. As a consequence, the…
The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…
We derive and analyze a hierarchy of approximations to the strongly correlated limit of the Hohenberg-Kohn functional. These "density representability approximations" are obtained by first noting that in the strongly correlated limit,…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…
We investigate properties of holomorphic extensions in the one-variable case of Whitney's Approximation Theorem on intervals. Improving a result of Gauthier-Kienzle, we construct tangentially approximating functions which extend…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
Convenient Cutkosky-like diagrammatic rules for computing the spectral densities of arbitrary two-point correlation functions in finite temperature field theory are derived. The approach is based on an explicit analytic continuation of…
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European…
We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…