Constructing estimates for stationary probabilities of states of the systems for which conditions close to those of I. N. Kovalenko theorem hold (Q580826)

In recent years a great number of works have appeared on the study of the invariance of characteristics of systems relative to the form of distribution functions for random variables that determine the operation of the systems. However, the class of systems for which the above-mentioned invariance conditions hold is relatively small. Much larger is the class of systems for which conditions close to invariance conditions hold. In that case the corresponding stationary probabilities of states are also close. In particular, this class contains the systems for which the rates of failure of elements are known not exactly but approximately. In the author, Dopov Akad Nauk Ukr. RSR, Ser. A 1979, 505-510 (1979; Zbl 0412.60089) this idea was realized for a system consisting of two elements. In this article those results are generalized for a more general scheme considered in \textit{I. N. Kovalenko}, Probl. Peredachi Inform. 11, 147-151 (1962; Zbl 0138.118). For any state of the system we obtain estimates of the difference between the corresponding stationary probabilities to within o(\(\epsilon)\). In constructing the estimates an essential role is played by the analytic-statistical method.