Related papers: On the Convergence of Random Fourier-Jacobi Series…
``Orderly divergence'' deals with limit theorems for weighted stochastic Gamma integrals of otherwise nonintegrable functions. Although for monotonic functions this category usually coincides with the classical notion of weighted limit…
In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in…
In this paper we introduce and discuss some classes of orthogonal polynomials in several non-commuting variables. The emphasis is on a non-commutative version of the orthogonal polynomials on the real line. We introduce recurrence equations…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…
Four Jacobi settings are considered in the context of Hardy's inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy's inequality is proved for the type…
We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…
We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvature motion and others describing…
This article presents and reviews several basic properties of the Cumulative Ord family of distributions; this family contains all the commonly used discrete distributions. A complete classification of the Ord family of probability mass…
Within the last fifteen years, a program of establishing relationships between algorithmic randomness and almost-everywhere theorems in analysis and ergodic theory has developed. In harmonic analysis, Franklin, McNicholl, and Rute…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of…
Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…
We provide sufficient conditions on the profile $\varphi$, on the sequence of random variables $\varepsilon_j>0$ and on the sequence of random vectors $y_j\in\mathbb{R}^n$ such that…
We develop a theory of Jacobi polynomials for parabolic subgroups of finite reflection groups that specializes to the cases studied by Heckman and Opdam in which the whole group and the trivial group are considered. For the intermediate…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…