Related papers: Computing lower expectations with respect to total…
The purpose of this paper is to find pointwise representation formulas for the density of the pairing between divergence-measure fields and BV functions, in this way continuing the research started in [17,20]. In particular, we extend a…
We provide optimal lower and upper bounds for the augmented Kullback-Leibler divergence in terms of the augmented total variation distance between two probability measures defined on two Euclidean spaces having different dimensions. We call…
Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and…
The inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions [1-4]. Using Taylor's frozen field hypothesis, we investigate the statistical properties of…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
Reduced chi-squared is a very popular method for model assessment, model comparison, convergence diagnostic, and error estimation in astronomy. In this manuscript, we discuss the pitfalls involved in using reduced chi-squared. There are two…
We analyze the one-dimensional semi-classical Schr\"odinger equation on the half-line with a linear potential and Dirichlet boundary conditions. Our main focus is on establishing improved dispersive and Strichartz estimates for this model,…
We derive a closed-form solution for the Kullback-Leibler divergence between two Fr\'echet extreme-value distributions. The resulting expression is rather simple and involves the Euler-Mascheroni constant.
In this paper, we define the generalized Wasserstein distance for sets of Borel probability measures and demonstrate that the weak convergence of sublinear expectations can be characterized by means of this distance.
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution…
Many important values for cooperative games are known to arise from least square optimization problems. The present investigation develops an optimization framework to explain and clarify this phenomenon in a general setting. The main…
We derive an analytical closed expression to compute the minimum distance (quantified by the angle of separation measured from the center of the Earth) between any two satellites located at the same altitude and in circular orbits. We also…
We establish derivative estimates of solution of elliptic system in narrow regions.
For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…
For a given $x$ we consider the minimum of $\sum_{n\le x} \chi(n)/n$ as $\chi$ ranges over all quadratic Dirichlet characters. For all large $x$, this minimum is negative and we give upper and lower bounds for it.
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
The purpose of this note is to prove dispersive estimates for the wave equation outside a ball in R^d. If d = 3, we show that the linear flow satisfies the dispersive estimates as in R^3. In higher dimensions d $\ge$ 4 we show that losses…
Let $S_n^\lambda$ be the set of all permutations over the multiset $\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where $n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of…
We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…