Abstract
The article is devoted to the use of random processes, which are one of the main sections of probabilistic modeling, in the economic and mathematical fields. A random process is a mathematical probabilistic model used to describe random events that often occur in time or coordinates. This is why, in recent years, some natural sciences have begun to use the theory of random processes in their respective fields. The article presents the concepts of determining the probabilities of the development of a situation from one stage to another for a homogeneous Markov chain (Markov process) in a system, based on the theoretical foundations of discrete Markov processes in the financial and economic system. As an example of the application of these conclusions, an analytical report of the banking system was considered. The desired probabilities of the final state were determined using two methods: the initial probability distribution matrix, the path vector matrix, and the transition probability matrix.