Illia Donhauzer

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20202026

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math.PR2026

Asymptotics of multifractal products of spherical random fields

Illia Donhauzer

The paper studies multifractal random measures on the sphere $S^{d}$ constructed via multifractal products of random fields. It presents new limit theorems for multifractal…

math.PR2025

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…

math.PR2023

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…

math.PR2022

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…

math.PR2021

Asymptotics of running maxima for $φ$ -subgaussian random double arrays

Nour Al Hayek, Illia Donhauzer, Rita Giuliano +2

The article studies the running maxima $Y_{m, j} = max_{1 \leq k \leq m, 1 \leq n \leq j} X_{k, n} - a_{m, j}$ where ${X_{k, n}, k \geq 1, n \geq 1}$ is a double array of $φ$ -subgaussian ra…

math.PR2020

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…