METHOD FOR ANALYSING NON-ERGODIC MARKOV SYSTEMS
Лев Григорьевич Раскин, Larysa Sukhomlyn, Dmytro Sokolov, Vitalii Vlasenko · Automation technological and business processes · 2025
Abstract. The object of study is a non-ergodic Markov system functioning under conditions when there is a subset of absorbing states among the set of possible states. The relevance of the problem is determined by the impossibility of analysing such systems by traditional methods. A high practical need for solving these problems arises to ensure the required efficiency of complex systems. Accordingly, the aim of the research is to develop a simple, convenient and efficient method for analysing non-ergodic Markov systems. The method of solving the problem proposed in this paper consists in transforming the original non-ergodic system into an ergodic one. The essence of the method consists in adding to the set of possible transitions of the system fictitious transitions from absorbing states to return states. In this case, the original non-ergodic system is transformed to an ergodic system available for analysis in the standard way. Thus, the proposed method solves the problem. The advantage of the method is simplicity of implementation and practical independence of the computational procedure from the dimensionality of the problem.