Application of markov random processes in probabilistic modeling of economic systems

The article is devoted to probabilistic statistical methods for modeling economic systems, as well as the theoretical foundations of probabilistic methods. The use of Markov random processes, which play a key role in probabilistic modeling, in the context of economic and mathematical research is considered. The Markov process is a mathematical model that allows you to describe random events that occur in time or space, which makes it especially relevant for analyzing the dynamics of economic systems. In recent years, there has been a growing interest in the theory of Markov processes in various fields of natural sciences. The article focuses on concepts related to determining the probabilities of transition from one state to another within a homogeneous Markov chain. These concepts are based on the theoretical foundations of discrete Markov processes and their application in financial and economic systems. As an illustration of the application of these theoretical conclusions, an analysis of the banking system was carried out. Two methods were used to determine the probabilities of reaching a finite state: the first is based on the original probability distribution matrix, and the second is based on the path vector matrix and the transition probability matrix. Both approaches resulted in identical results, confirming their reliability. The obtained probabilistic estimates allow not only to predict possible scenarios for the development of the economic system, but also to make informed decisions to optimize it. Thus, Markov random processes become an important tool for forecasting and analysis in the field of economics.