On Quasiinvariant Distributions on Uniform Arrays

The article examines Markov chains of a special type with a continual set of states, which describe the behavior of multicomponent systems. A small stochastic noise is superimposed on the deterministic transformation that eliminates any finite perturbations of some initial state. It is shown that for such chains there exist probability distributions that are “similar” to the initial state and that change only slightly with time.