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This article is cited in 1 scientific paper (total in 1 paper)
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
Citation:
V. F. Gaposhkin, “Precise estimates of the metric entropy for the set of arithmetic averages of quasi-stationary processes”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 785–793; Theory Probab. Appl., 51:4 (2007), 695–704
Linking options:
https://www.mathnet.ru/eng/tvp26https://doi.org/10.4213/tvp26 https://www.mathnet.ru/eng/tvp/v51/i4/p785
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