44 citations · 255 across the 35 of their papers we have counts for
45 papers
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…