相关论文: About the value of the two dimensional Levy's cons…

We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the…

The main goal of the work is to study the stochastic averaging principle for two time-scales stochastic evolution equations driven by L\'evy process. The solution of reduced equation with modified coefficient is derived to approximate the…

We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine…

We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {-1,1}^n. This result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the…

This paper develops the metric theory of simultaneous inhomogeneous Diophantine approximation on a planar curve with respect to multiple approximating functions. Our results naturally generalize the homogeneous Lebesgue measure and Hausdor?…

We obtain an intertwining relation between some Riemann-Liouville operators of order a in (1,2) connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric a-stable L\'evy…

In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context.…

We prove an optimal Hardy inequality for the fractional Laplacian on the half-space.

In this paper we study the three-dimensional analogue of the relation between the irrationality exponent of a real number and the growth of its regular continued fraction partial quotients. As a multidimensional generalisation of continued…

The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…

The value function associated with an optimal control problem subject to the Navier-Stokes equations in dimension two is analyzed. Its smoothness is established around a steady state, moreover, its derivatives are shown to satisfy a Riccati…

The paper concerns the uniform polynomial approximation of a function $f$, continuous on the unit Euclidean sphere of ${\mathbb R}^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First we…

The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m : a<Q[m]<b\}$, which are restricted to rescaled and growing domains $r\;\Omega$, is approximated by the volume. An effective error bound of order…

In this work, we present a comprehensive study of the relationship among uniform Lyapunov exponents, the Liouville trace formula, and adapted metrics for cocycles in Hilbert spaces. First, we prove that uniform Lyapunov exponents can be…

We examine a possibility to introduce a non-trivial classical background metric into the 2-d Liouville gravity theory. The classical background appears as a part of the Weyl factor of the physical metric of 2-d surfaces with some conformal…

The present paper is devoted to the proof of time decay estimates for derivatives at any order of finite energy global solutions of the Navier-Stokes equations in general two-dimensional domains. These estimates only depend on the order of…

We consider finite element approximations to the optimal constant for the Hardy inequality with exponent $p=2$ in bounded domains of dimension $n=1$ or $n \geq 3$. For finite element spaces of piecewise linear and continuous functions on a…

An upper bound for the Lebesgue constant (the supremum norm) of the operator of interpolation of a function in equally spaced points of a triangle by a polynomial of total degree less than or equal to n is obtained. Earlier, the rate of…

Rio gave a concise bound for the central limit theorem in the Vaserstein distances, which is a ratio between some higher moments and some powers of the variance. As a corollary, it gives an estimate for the normal approximation of the small…

We provide representations of Euler's constant $\gamma=0.577...$ as series which converge geometrically fast (but use coefficients whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are discussed.