arXiv subjects

Illia Donhauzer

Publications and source records attributed to Illia Donhauzer.

9 recordsLinked to original sources

arXiv2026

Asymptotics of multifractal products of spherical random fields

The paper studies multifractal random measures on the sphere $\mathbb{S}^d$ constructed via multifractal products of random fields. It presents new limit theorems for multifractal products of spherical fields and conditions for the non-degeneracy of the limiting measure. The multifractal properties of the limiting measure are investigated, and its Rényi function is derived. Compared to earlier results on multifractal products of spherical fields, the obtained limit theorems hold under general mixing conditions, enabling the consideration of multifractal products of fields from a broad class and the construction of random measures with flexible multifractal properties.

math.PR↗

arXiv2026

Anomaly prediction in XRP price with topological features

The aim of this research is to study XRP cryptoasset price dynamics, with a particular focus on forecasting atypical price movements. Recent studies suggest that topological properties of transaction graphs are highly informative for understanding cryptocurrency price behavior. In this work, we show that specific topological properties of the XRP transaction graphs provide important information about extreme XRP price surges, and can be used for more competitive prediction of anomalous price dynamics.

q-fin.ST↗

arXiv2026

Extended Isolation Forest with feature sensitivities

Compared to theoretical frameworks that assume equal sensitivity to deviations in all features of data, the theory of anomaly detection allowing for variable sensitivity across features is less developed. To the best of our knowledge, this issue has not yet been addressed in the context of isolation-based methods, and this paper represents the first attempt to do so. This paper introduces an Extended Isolation Forest with feature sensitivities, which we refer to as the Anisotropic Isolation Forest (AIF). In contrast to the standard EIF, the AIF enables anomaly detection with controllable sensitivity to deviations in different features or directions in the feature space. The paper also introduces novel measures of directional sensitivity, which allow quantification of AIF's sensitivity in different directions in the feature space. These measures enable adjustment of the AIF's sensitivity to task-specific requirements. We demonstrate the performance of the algorithm by applying it to synthetic and real-world datasets. The results show that the AIF enables anomaly detection that focuses on directions in the feature space where deviations from typical behavior are more important.

stat.ME↗

arXiv2025

Construction and limit theorems for supCAR fields

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 infinitely divisible marginal distributions. Their second-order properties are characterised by a novel family of covariance functions which can exhibit short- and long-range spatial dependencies. First, the existence of such fields is examined. Then, functional limit theorems for supCAR fields are derived under general assumptions. Four limiting scenarios that depend on the marginals of the underlying autoregressive fields and the specifications of the superposition are identified. Examples of specific supCAR fields, for which the assumptions and results are provided in simple, explicit forms, are presented. The obtained limit theorems can be employed for the statistical inference of supCAR fields.

math.PR↗

arXiv2023

Stochastic diffusion within expanding space-time

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 where the expansion of space-time is used in modelling various phenomena. Contrary to other results in the literature, the considered in this paper general stochastic model takes into consideration the expansion of space-time. It leads to a stochastic diffusion equations with coefficients that are non-constant and evolve with the expansion factor. Then, the Cauchy problem with random initial conditions is posed and investigated. The exact solution to a stochastic diffusion equation on the expanding sphere is derived. Various probabilistic properties of the solution are studied, including its dependence structure, evolution of the angular power spectrum and local properties of the solution and its approximations by finite truncations. The paper also characterises the extremal behaviour of the random solution by establishing upper bounds on the probabilities of large deviations. Numerical studies are undertaken to illustrate the obtained theoretical results and demonstrate the evolution of the random solution.

math.PR↗

arXiv2022

Limit theorems for multifractal products of random fields

This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of convergence of cumulative fields are presented. Simple unified conditions for the limit theorems and the calculation of the Rényi function are given. They are less restrictive than those in the known one-dimensional results. The developed methodology is also applied to multidimensional multifractal measures. Finally, a new class of examples of geometric $φ$-sub-Gaussian random fields is presented. In this case, the general assumptions have a simple form and can be expressed in terms of covariance functions only.

math.PR↗

arXiv2021

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

The article studies the running maxima $Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}$ where $\{X_{k,n}, k \ge 1, n \ge 1\}$ is a double array of $φ$-subgaussian random variables and $\{a_{m,j}, m\ge 1, j\ge 1\}$ is a double array of constants. Asymptotics of the maxima of the double arrays of positive and negative parts of $\{Y_{m,j}, m \ge 1, j \ge 1\}$ are studied, when $\{X_{k,n}, k \ge 1, n \ge 1\}$ have suitable "exponential-type" tail distributions. The main results are specified for various important particular scenarios and classes of $φ$-subgaussian random variables.

math.PR↗

arXiv2020

Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances

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 domain asymptotics is studied. Conditions to guarantee that the Strong Law of Large Numbers holds true are provided. The considered scenarios include wide classes of non-stationary random fields. The discussion about application to weak and long-range dependent random fields and numerical examples are given.

math.PR↗

arXiv2020

On stationarity properties of generalized Hermite-type processes

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 case of increasing multidimensional domain asymptotics is studied. Three approaches to investigate properties of these processes are discussed. Contrary to the classical one-dimensional case, it is shown that for any choice of a multidimensional observation window the generalized Hermite-type process has non-stationary increments.

math.PR↗