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Short Communications

Precise estimates of the metric entropy for the set of arithmetic averages of quasi-stationary processes

V. F. Gaposhkin

Moscow State University of Railway Communications

Abstract: Estimates of the $\varepsilon$-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 $\varepsilon\to+0$.

Keywords: stationary and quasi-stationary sequences, $R$-systems, arithmetic average, $\varepsilon$-entropy of the sets of arithmetic averages, upper and lower estimates.

Received: 15.06.2005
Revised: 15.05.2006

DOI: 10.4213/tvp26

 English version: Theory of Probability and its Applications, 2007, 51:4, 695–704

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