We consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on nonnegative axis by dependent data. We use the class of kernel estimators with asymmetric gamma kernel functions. The gamma kernels are nonnegative; they may change their shape depending on the position on the semi-axis and possess good boundary properties for a wide class of densities. Asymptotic estimates of the multivariate density and of its partial derivatives such as biases, variances, and covariances are derived. The optimal bandwidth of both estimates is obtained as a minimum of the mean integrated squared error (MISE) by dependent data with a strong mixing. Optimal convergence rates of the MISE both for the density and its derivative are found.

The article aims to identify the size, prospects and purpose of the digital economy. Based on the methodology of analysis and synthesis, structuring of scientific positions using a systematic approach, abstract and logical types of analysis and analysis of statistical data, the author reveals the problem of the need to form a system of special knowledge about the essence and principles of digital economy functioning, which should be formulated by specialists in the basic and applied economic sciences and allow to create a basis for a systematic scientific-based multi-parameter study of the digital economy continuum. However, the study shows that the digital economy, including its digital segment, shows a slower growth than previously expected and predicted. There is also a lag in the rate of development of the biotechnology industry. Yet, this does not call into question that the digital economy will develop at a faster pace in the near future. The result is an empirically based conclusion that, while the actual size of the digital economy is small relative to the size of all world production, the growth rate of digital technologies is exponentially increasing, expanding the space of the digital economy. For quality transformation, the underlying digital technology needs socialization, which implies the development of the technology itself, its size and acceptance by society. As a result of socialization, the most important general purpose of the digital economy—to meet the needs of consumers, and its special purpose—to contribute to the development of human capital, improve the quality of life of individuals, countries and the entire population of the planet, as well as reduce the uneven development of regions of the planet and economic sectors, should be fulfilled.

Usually, DEA methods are used for the assessment of a region’s disaster vulnerability. However, most of these methods work with precise values of all the characteristics of the regions. At the same time, in real life, quite often most of the data consists of expert estimates or approximate values. In this regard, we propose to use modified DEA methods, which will take into account inaccuracy of the data. We apply these methods to the evaluation of wildfire preventive measures in the Russian Federation regions.

In modern conditions, requirements for the level of training of analysts, the need for training experts for modern decision support centers for managing business systems (situational centers) requires the use of modern educational technologies that can use the information accumulated in the systems, experience analysis and problem-solving, external sources for the formation of skills and abilities to analyze in new or complex crisis situations and the preparation of appropriate management decisions.

This article proposes an approach to security provision of one of the key bases of digital transformation – the technology of the Internet of things (IoT). The effective technology of carrying out the information security audit with application of Honeypot systems is the cornerstone of the article and the offered method. The main advantages of the use of container virtualization, unlike application of traps on the basis of virtual machines, are formulated by the authors. The method of protection of a similar infrastructure by means of integration of dynamic container virtualization of network traps is considered. The article contains information on implementation of the offered method, comparison of results with existing solutions, and a summary table with the actual results of an experiment. A detailed flowchart of functioning of the offered method is also provided in the work. The proposed solutions allow to increase efficiency of the malefactor’s actions analysis. The administrator of IoT devices network can obtain information about the priority purposes, the used by malefactor means, and vulnerabilities of various elements of network. These circumstances give an opportunity to quickly take measures for increase in security of network and to avoid its compromise.