On the central limit theorem for homogeneous discrete-time nonlinear Markov chains

The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are characterized by complex limit behavior and ergodic properties, for which the usual criteria for Markov processes are not sufficient. Being a subclass of nonlinear Markov processes, nonlinear Markov chains have inherited these features. In this paper, conditions for the fulfillment of the central limit theorem for homogeneous nonlinear Markov chains in discrete time and with a discrete finite state space are studied. Also, a brief review of known results on the ergodic properties of nonlinear Markov chains is included. The obtained result complements the existing results in this area and may be useful for further applications in statistics.Comment: in Russian languag

Overgroups of elementary block-diagonal subgroups in even unitary groups over quasi-finite rings

Shchegolev A. Overgroups of elementary block-diagonal subgroups in even unitary groups over quasi-finite rings. Bielefeld: University of Bielefeld; 2015

Territorial Public Self-Government as an Element of Political Infrastructure for Secure Development of Municipal Sections in the Conditions of Digitalization

The research is devoted to the topic of forming a political infrastructure for the safe development of municipalities, creating technologies for attracting political infrastructure participants to the development and assessment of alternatives for the optimal development of territories.We set ourselves the goal of showing territorial public self-government as a tool for increasing the openness of political decision-making and public confidence in the authorities, and identifying the transformational potential of digital technologies in the context of territorial public self-government.The methodological basis of the research was provided by such theories as: the information cybernetic model of the political system of K. Deutsch, the theory of the political system of D. Easton, the theory of deliberative democracy by J. Besset, the theory of direct democracy I. Blo, model of monitor (digital) democracy by J. Keane.The main results of this study are the following:1) the author’s definition of the concept of “digitalization” was introduced — this is a process of radical transformation of the interaction of people in all spheres of social life, the implementation of which became possible on the basis of replacing analog (physical) data collection and processing systems with new technological systems that generate, transmit and process a digital signal about your condition. This transformation presupposes the formation of a different outlook of citizens, the use of other methods of management;2) the author’s definition of the concept of “political infrastructure” is introduced — these are the types of connections between the elements of the political system. Different types of ties form various modifications of political institutions, they determine the contours of political communications carried out in the political space, including using various political technologies to influence the behavior of political forces.3) in the context of digitalization, interactive interaction of participants in the political process, the very configuration of the political infrastructure for the development of territories is changing, the political toolkit of dialogue between the authorities and society is changing, implying an increasingly widespread use of technologies to involve participants in political processes in the development and assessment of alternatives for optimal territorial development