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We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums over a rectangular grid of dimension $d$ of a random field satisfying a weak dependency assumption of projective type: the difference between the expectation…
We study the problem of estimating time-varying coefficients in ordinary differential equations. Current theory only applies to the case when the associated state variables are observed without measurement errors as presented in…
We study the weak convergence of iterates of so-called centred kernel quadratic stochastic operators. These iterations, in a population evolution setting, describe the additive perturbation of the arithmetic mean of the traits of an…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output…
We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty…
The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and…
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…
We obtain non-uniform Berry-Esseen type estimates for several classes of weakly dependent sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or expanding…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex brownian motion and the…
We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result…
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
Varying-coefficient functional linear models consider the relationship between a response and a predictor, where the response depends not only the predictor but also an exogenous variable. It then accounts for the relation of the predictors…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…