arXiv subjects

Oleksandr Liubimov

Publications and source records attributed to Oleksandr Liubimov.

4 recordsLinked to original sources

arXiv2026

Polynomial regression under a mixture of classical and Berkson errors

A polynomial structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors, as well as some of their higher moments are assumed to be known. Without normality assumptions, consistent estimators of model parameters are constructed using the Corrected Score method, and conditions for their asymptotic normality are given. Under mild conditions, we found pairs of asymptotically independent estimators. A simulation study illustrates the results.

math.ST↗

arXiv2025

Boundedness of solutions of the first-order linear multidimensional difference equations

We investigate the boundedness of solutions of the first order linear difference equation of the form $x_{n+1} = Ax_{n} + y_{n}, \; n \geq 1$ where $A$ is a square matrix with complex entries, sequence $\{y_{n}\}_{n\geq 1}$ and initial value $x_1$ are supposed to be known. Firstly, we discuss the one-dimensional case of this equation $x_{n+1} = ax_{n} + y_{n}, \; n \geq 1$ where $a$ is a complex number. In particular, we obtain the sufficient conditions for boundedness or unboundedness of the solutions in case $|a|=1$(the critical case) by considering the exponential sums of the forms $\sum y_{n}e(nφ)$ and $\sum e(f(n))$. Then we proceed to the investigation of the equation in the multidimensional case and reduce our problem to analysis of the spectrum and Jordan cells of matrix $A$. The problem is especially interesting when spectrum of $A$ contains eigenvalues $λ$ with $|λ|=1$. At the end of the article we obtain a theorem that reveals the connection between equations $x_{n+1} = ax_{n} + y_{n}, \; n \geq 1$ with $|a|=1$ and $x_{n+1} = Jx_{n} + y_{n}, \; n \geq 1$ with $J$ being a Jordan cell of an eigenvalue $λ$, $|λ|=1$.

math.DS↗

arXiv2025

Ergodic approach to the study of boundedness of solutions of one type of the first-order semilinear difference equations

We investigate the sufficient conditions for boundedness of one type of difference equations of the form $x(n+1)=ax(n)+f(x(n)) + y(n), \ n\geq 1$ in critical case $|a|=1$. For this equation the following assumptions are introduced: 1) The function $f: \mathbb{C} \to \mathbb{C}$ and the input sequence $\{y(n)\}_{n\geq1}$ are assumed to be bounded. 2) $\text{Re}\left(\overline{f(ρ\, e^{2πi θ})} \; \cdot ae^{2πi θ}\right)$ converges uniformly on $[0,1) \ni θ$ to some real-valued function $Φ(θ)$ as $ρ\to +\infty$ . Combining the celebrated results of the probability and ergodic theory together with the geometric consideration of the problem, we show that under fairly general conditions this type of semilinear difference equations has all the solutions bounded. Subsequently we formulate the quantitative version of our theorem and give the example of its application. In addition, in the last section we discuss the conditions of our main result and provide the constructions, which highlight the importance of these conditions.

math.DS↗

arXiv2025

Modeling CubeSat Storage Battery Discharge: Equivalent Circuit Versus Machine Learning Approaches

The subject of the article is the study and comparison of two approaches to modelling the battery discharge of a CubeSat satellite: analytical using equivalent circuit and machine learning. The article aims to make a reasoned choice of the approach to modelling the battery discharge of a CubeSat satellite. Modelling the battery discharge of a satellite will enable the prediction of the consequences of disconnecting the autonomous power system and ensure the fault tolerance of equipment in orbit. Therefore, the selected study is relevant and promising. This study focuses on the analysis of CubeSat satellite data, based explicitly on orbital data samples of the power system, which include data available at the time of the article publication. The dataset contains data on the voltage, current, and temperature of the battery and solar panels attached to the five sides of the satellite. In this context, two approaches are considered: analytical modelling based on physical laws and machine learning, which uses empirical data to create a predictive model. Results: A comparative analysis of the modeling results reveals that the equivalent circuit approach has the advantage of transparency, as it identifies possible parameters that facilitate understanding of the relationships. However, the model is less flexible to environmental changes or non-standard satellite behavior. The machine learning model demonstrated more accurate results, as it can account for complex dependencies and adapt to actual conditions, even when they deviate from theoretical assumptions.

cs.SE↗