«modulus of continuity»

Linear multifractional multistable motion: LePage series representation and modulus of continuity

In this paper, we obtain an upper bound of the modulus of continuity of linear multifractional multistable random motions. Such processes are generalizations of linear multifractional α-stable motions for which the stability index α is also allowed to vary in time. In the case of

On genuine Lupac{s}-Beta operators and modulus of continuity

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention results on the weighted modulus

A Clt for the L2 Modulus of Continuity of Brownian Local Time1 By

Let {L x t ; (x, t) ∈ R 1 × R 1 + } denote the local time of Brownian motion, and α t := ∞ −∞ (L x t) 2 dx. Let η = N(0, 1) be independent of α t. For each fixed t, ∞ −∞ (L x+h t − L x t) 2 dx − 4ht h 3/2 L → 64 3 1/2 √ α t η as h → 0. Equivalently, ∞ −∞ (L x+1 t − L x t) 2 dx −

A CLT for the L modulus of continuity of Brownian local time

Let {Lt ; (x, t) ∈ R1 ×R1 +} denote the local time of Brownian motion and αt := ∫ ∞ −∞ (Lt ) 2 dx. Let η = N(0, 1) be independent of αt. For each fixed t ∫∞ −∞(L x+h t − Lt )2 dx− 4ht h3/2 L → ( 64 3 )1/2 √ αt η, as h → 0. Equivalently ∫∞ −∞(L x+1 t − Lt )2 dx− 4t t3/4 L → ( 64 3

Majorization of the Modulus of Continuity of Analytic Functions

Let G be a bounded domain in the complex plane, let f be analytic in G and continuous in G, and let μ be a majorant, that is, a non-negative non-decreasing function defined for t ≥ 0 such that μ(2t) ≤ 2μ(t) for all t ≥ 0. Suppose that z1 ∈ ∂G and that |f(z1) − f(z2)| ≤ μ(|z1 − z2

Modulus of continuity on parts of the boundary and solid modulus of continuity

On L2 modulus of continuity of Brownian local times and Riesz potentials

Stochastic integral representation of the L modulus of Brownian local time and a central limit theorem

The purpose of this note is to prove a central limit theorem for the L -modulus of continuity of the Brownian local time obtained in [2], using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight’s theorem and the Clark-Ocone f

Moduli of Continuity and Average Decay of Fourier Transforms: Two-sided Estimates and a Cantor Type Example

Following D. B. H. Cline [Cl], we study the connections between the behavior of the spherical mean of an L modulus of continuity corresponding to the finite difference of an arbitrary order m > 0 of a function f ∈ L(R), 1 ≤ p ≤ ∞, d ∈ N, and the average decay of the Fourier trans

Optimal approximation of continuous functions by very deep ReLU networks

We prove that deep ReLU neural networks with conventional fully-connected architectures with W weights can approximate continuous ν-variate functions f with uniform error not exceeding aνωf (cνW −2/ν), where ωf is the modulus of continuity of f and aν , cν are some ν-dependent co