Bulletin of the Taras Shevchenko National University of Kyiv. Physics and Mathematics

Even though the problem of modelling and simulation is not new it continues to be actual over time. Our computers are becoming more powerful and this allows us to use more sofisticated algorithms for more complicated problems. In this paper we constructed the model from the series decomposition of the Gaussian stationary Ornstein–Uhlenbeck process. The Ornstein-Uhlenbeck process is widely used to model reversal processes, exchange rates, asset price volatility, etc. Controlling the model’s accuracy and reliability with which it approximates the real process is important for applications. For this purpuse we have established the relation between the model’s erorr measured in the norm of Lp-space and accuracy and reliability. The classical methods and results from the general theory of stochastic processes and sub-Gaussian spaces of random variables were used in our research. Since Gaussian stochastic processes are sub-Gaussian as well, we can utilize them. For one particular case the calculations were made in order to show how our results can be used in the particular situations. The results from our paper can help to simulate and analyse the situations which the Ornstein–Uhlenbeck process fits well.

Tetiana Ianevych

Olga Vasylyk

Julia DOSHCHUK

Bulletin of Taras Shevchenko National University of Kyiv Series Physics and Mathematics

On modeling gaussian stationary Ornstein–Uhlenbeck processes with given reliability and accuracy in Lp-spaces

关于在Lp空间中建模具有给定可靠性和精度的高斯平稳Ornstein-Uhlenbeck过程

Background. Random process theory is being used more and more in various fields of science due to the high computing power of modern computers. However, it's often important to know how much we can rely on the models we use. Methods. This paper examines the modelling of the fractional Brownian motion with given accuracy and reliability. The modelling is based on Dzhaparidze and van Zanten series representation of the fractional Brownian motion. We consider the fractional Brownian motion as an input process to a time-invariant linear system with a real-valued square-integrable impulse response function, which is defined on the finite domain. Results. We prove the theorem that gives the conditions, specifically the value of the upper limit of the summing in the model, under which the obtained model approximates fractional Brownian motion with given accuracy and reliability taking into account the response of the system. Conclusions. For the proof, we use the properties of square-Gaussian stochastic processes.

Iryna Rozora

Yevhenii Sheptukha

Simulation of the fractional Brownian process with given accuracy and reliability

给定精度和可靠性的分形布朗过程模拟

Analyzing macroeconomic indicators and their impact on a country's global rating is crucial for understanding economic stability and international status. This study focuses on such indicators as GDP, external debt, and inflation, which are critical to Ukraine's economic stability and international rating. The study utilized correlation analysis and the development of sophisticated linear regression models to quantitatively assess the impact of various economic indicators on Ukraine's international rating. This methodological approach reveals the complex relationships between economic activity and global evaluation The findings emphasize the importance of comprehensive economic analysis in strategic planning and policy formulation. It was found that GDP, external debt, and inflation significantly impact the country's rating. Additionally, the research lays a foundational framework for analyzing the impact of economic indicators on a country's rating, paving the way for future investigations into the predictive capabilities of economic models in global assessments. Features of the transformation of macroeconomic indicators into a country's rating are presented in two main directions: influence on investment attractiveness and economic confidence in the country. The study confirms the critical role of macroeconomic analysis in deciphering and enhancing a country's international standing.

Volodymyr Zubchenko

Mariia Herasymenko

Analysis of the impact of macroeconomic indicators on the country's rating

宏观经济指标对国家评级影响的分析

The work explores the asymptotic properties of large-dimensional stochastic matrices N under the condition of independence of matrix elements or rows (columns). An analysis of the main properties of eigenvalues of stochastic matrices is conducted. The work is dedicated to investigating the asymptotic characteristics of random matrices under the absence of the second moment and also considers the presence of "heavy tails" in the corresponding transitions in the adjacency matrices of the respective graph. The main result of the work is formulated in terms of the transition matrix of a discrete Markov chain and its eigenvalues. In proving the theorem, a non-degenerate Markov chain is considered, describing a mathematical model of random processes that do not change over time with known transition probabilities between states and a corresponding stochastic matrix P, one of whose eigenvalues is unity, and all eigenvalues of the stochastic matrix do not exceed it in absolute value. The proof of this fact follows from the Perron–Frobenius theorem, which concerns the properties of positive matrices and their eigenvalues. Thus, the theorem considered manages to expand the class of random matrices A for which convergence of eigenvalues of the matrix can be applied under the conditions imposed on the elements of the adjacency matrix. Moreover, the imposed conditions are relaxed compared to classical results, where the existence of a finite second moment for the elements of the adjacency matrix is required. This result generalizes both classical results for the normal distribution and similar results of other authors. The obtained result can be used in graph clustering problems to choose the optimal number of clusters, namely, they can be applied to determine the optimal number of clusters in a Grid system, complex networks, in investigations of the structure of the web space, etc.

Oksana Kyrychenko

Yevhen Kyrychenko

Asymptotic properties of random matrices

随机矩阵的渐近性质

The prevalence of diabetes is constantly increasing, and timely diagnosis of this disease is extremely important in the health care system. Nowadays, in addition to advanced medical technologies, there is an opportunity to process large volumes of information quickly and efficiently, in particular medical information. Patients with diabetes, even in the early stages, have certain similar symptoms and patterns, which makes it possible to effectively diagnose the disease, based on easily obtained clinical data. In this work, we compare the accuracy of different machine learning algorithms for diagnosing diabetes on binary data that do not include laboratory tests, and can be obtained by patient questionnaires. All the classification models give good results and show the feasibility of identifying individuals probably having undiagnosed diabetes, based on questionnaire data. The best results are provided by random forest classifier. In order to improve the accuracy of the classification, an analysis of the relationships between the variables of the dataset was carried out. This made it possible to reduce the dimensionality of the model by removing variables that do not carry useful information. Moreover, the data set is additionally balanced. The resulting models demonstrate higher efficiency than the classification models built on the base dataset.

Hanna Livinska

Daria Skrypnyk

José Luis Galán-García

Comparative study of machine learning algorithms for diabetes detection using binary data

基于二值数据的糖尿病检测机器学习算法比较研究

Publication Information	Publisher: Taras Shevchenko National University of Kyiv，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2019，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:
Journal Fees	$Details
Average review cycle	12 weeks

Bulletin of the Taras Shevchenko National University of Kyiv. Physics and Mathematics

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On modeling gaussian stationary Ornstein–Uhlenbeck processes with given reliability and accuracy in Lp-spaces

Simulation of the fractional Brownian process with given accuracy and reliability

Analysis of the impact of macroeconomic indicators on the country's rating

Asymptotic properties of random matrices

Comparative study of machine learning algorithms for diabetes detection using binary data

On modeling gaussian stationary Ornstein–Uhlenbeck processes with given reliability and accuracy in Lp-spaces

Simulation of the fractional Brownian process with given accuracy and reliability

Analysis of the impact of macroeconomic indicators on the country's rating

Asymptotic properties of random matrices

Comparative study of machine learning algorithms for diabetes detection using binary data