44 citations · 255 across the 35 of their papers we have counts for
30 papers · 1 filter
Exploring the Structure of Anisotropic Random Fields on the Sphere
Claudio Durastanti, Shahid Khan, Andriy Olenko
This paper addresses fundamental questions about the existence and structure of isotropic and anisotropic spherical random fields and the properties of composite transformations of…
Multiscale Asymptotic Analysis of Kernel-Smoothed Solutions to Fractional Riesz-Bessel Equations with Random Initial Conditions
Shahid Khan, Andriy Olenko
This paper investigates fractional Riesz-Bessel equations with random initial conditions that exhibit either classical or cyclic long-range dependence. It studies zoom-in asymptoti…
On asymptotic behavior of solutions to random fractional Riesz-Bessel equations with cyclic long memory initial conditions
Maha Mosaad A. Alghamdi, Andriy Olenko
This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequenc…
Multiscaling asymptotic behavior of solutions to random high-order heat equations
Maha Mosaad A Alghamdi, Nikolai Leonenko, Andriy Olenko
This paper studies high-order partial differential equations with random initial conditions that have both long-memory and cyclic behavior. The cases of random initial conditions w…
Construction and limit theorems for supCAR fields
Illia Donhauzer, Nikolai Leonenko, Andriy Olenko
The paper introduces a new class of random fields, supCAR fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess in…
Multiscaling limit theorems for stochastic FPDE with cyclic long-range dependence
Maha Mosaad A Alghamdi, Nikolai Leonenko, Andriy Olenko
The paper studies solutions of stochastic partial differential equations with random initial conditions. First, it overviews some of the known results on scaled solutions of such e…
Stochastic diffusion within expanding space-time
Philip Broadbridge, Illia Donhauzer, Andriy Olenko
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology wh…
On Fractional Spherically Restricted Hyperbolic Diffusion Random Field
Nikolai Leonenko, Andriy Olenko, Jayme Vaz
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are give…
Limit theorems for multifractal products of random fields
Illia Donhauzer, Andriy Olenko
This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative…
Asymptotics of running maxima for -subgaussian random double arrays
Nour Al Hayek, Illia Donhauzer, Rita Giuliano +2
The article studies the running maxima where is a double array of -subgaussian ra…
Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances
Illia Donhauzer, Andriy Olenko, Andrei Volodin
The paper proves the Strong Law of Large Numbers for integral functionals of random fields with unboundedly increasing covariances. The case of functional data and increasing domai…
Reduction principle for functionals of strong-weak dependent vector random fields
Andriy Olenko, Dareen Omari
We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct ne…
On stationarity properties of generalized Hermite-type processes
Illia Donhauzer, Andriy Olenko
The paper investigates properties of generalized Hermite-type processes that arise in non-central limit theorems for integral functionals of long-range dependent random fields. The…
Analysis of Spherical Monofractal and Multifractal Random Fields
Nikolai Leonenko, Ravindi Nanayakkara, Andriy Olenko
The Rényi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the Rényi…
Spherically Restricted Random Hyperbolic Diffusion
Philip Broadbridge, Alexander D. Kolesnik, Nikolai Leonenko +2
This paper investigates solutions of hyperbolic diffusion equations in with random initial conditions. The solutions are given as spatial-temporal random fields. The…
Limit theorems for filtered long-range dependent random fields
Tareq Alodat, Nikolai Leonenko, Andriy Olenko
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernel…
Non-central limit theorems for functionals of random fields on hypersurfaces
Andriy Olenko, Volodymyr Vaskovych
This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in . We…
Reduction principle for functionals of vector random fields
Andriy Olenko, Dareen Omari
We prove a version of the reduction principle for functionals of vector long-range dependent random fields. The components of the fields may have different long-range dependent beh…
Weak convergence of weighted additive functionals of long-range dependent fields
Tareq Alodat, Andriy Olenko
We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the co…
On rate of convergence in non-central limit theorems
Vo Anh, Nikolai Leonenko, Andriy Olenko +1
The main result of this paper is the rate of convergence to Hermite-type distributions in non-central limit theorems. To the best of our knowledge, this is the first result in the…
Whittaker-Kotel'nikov-Shannon approximation of -sub-Gaussian random processes
Yuriy Kozachenko, Andriy Olenko
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it inves…
On the rate of convergence to Rosenblatt-type distribution
Vo Anh, Nikolai Leonenko, Andriy Olenko
The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for s…
Uniform convergence of compactly supported wavelet expansions of Gaussian random processes
Yuriy Kozachenko, Andriy Olenko, Olga Polosmak
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general cla…
Convergence rate of wavelet expansions of Gaussian random processes
Andriy Olenko, Yuriy Kozachenko, Olga Polosmak
The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.