Precise Estimates of the Metric Entropy for the Set of Arithmetic Averages of Quasi-Stationary Processes

摘要

Estimates of the ＄arepsilon$-entropy of the set of arithmetic averages for an＄R＄-quasi-stationary system are obtained depending on the decay rate of the function ＄R(n)＄. It is shown that the deduced estimates are the best in order as ＄arepsilon o +0＄.