Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article, the Modulated Fou

The aim of this work is to improve the complexity result for the large-update method. First, we present a new bi-parametric kernel function with a hyperbolic barrier term. Then using simple tools, we show that the complexity bound of the algorithm based o

We present the Gebelein inequality in a separable real Hilbert space. As an application we prove the Strong Law of Large Numbers for Gaussian functionals with values in a separable real Banach space.

This article aims to contribute to the theory of variable-power copulas. In the first part, we discuss and study two unexplored variable-power copulas based on a modification of the function "x 1/y y 1/x ". Their originality in definition offers interesting alternative options to the existing variablepower copulas. However, these copulas have a strong limitation: they are free of any parameters, making them rigid in the functional sense. In light of this, the second part is devoted to some parametric versions of them, still belonging to the variable-power copulas family. They have the feature of being original and of recovering the independence copula for some values of the parameter. Their properties are investigated. Copula theory, initially introduced by Sklar [14], has become a vital tool for analyzing multivariate data and characterizing the dependence structure between random variables. The main functions, called copulas, provide a means to separate the marginal distributions from the dependence structure, allowing practitioners to model and estimate the joint distribution independently. This flexibility has enabled copulas to find applications in a wide range of fields, including finance (see [9] ), insurance (see [7] ), environmental sciences (see [1] ), and many others. The main theoretical and applied background on copulas can be found in [12, 5] , and recent advancements are described in [15, 16, 3, 4, 2, 11, 13, 6, 18] . Nowadays, the need for new copula constructions arises due to several reasons. Firstly, existing copula families may lack the flexibility to model dependence structures with asymmetric tail behavior or extreme values, which

We compare the maximum principle and the linear quadratic regulator approach (LQR)/well-posedness criterion to mean variance hedging (MVH) when the wealth process follows a jump diffusion. The comparison is made possible via a measurability assumption on

We consider the initial boundary value problem for a Boussinesq-type equation with a logarithmic damping term and variable-exponent nonlinearities, which was introduced to describe some physical phenomena such as propagation of small amplitude and long waves on the surface of shallow water. The blow-up of solutions is proved for positive as well as negative initial energy.

The one-dimensional quantum harmonic oscillator is considered. The wave solution of the Schrödinger equation determines the model of motion of particles in the $n$-quantum state as orbits of a stationary random walk at the moment of jump from the $n-1$-qu

We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain as well as the solution to the Poisson equatio

The paper concerns a certain parameter selection criterion for a combination of Ritz approximation of an ill-posed problem and Tikhonov regularization in the case when the level of data noise is unknown. A new minimization-based noise-level-free choice ru

The motion of incompressible magnetohydrodynamics (mhd) in a domain bounded by a free surface and coupled through it with an external electromagnetic field is considered. Transmission conditions for electric currents and magnetic fields are prescribed on