This article is cited in 20 papers

Decrease rate of the probabilities of $\varepsilon$-deviations for the means of stationary processes

V. F. Gaposhkin

Moscow State University of Railway Communications

Abstract: The asymptotic behavior as $n\to\infty$ of the normed sums $\sigma_n=n^{-1}\sum_{k=0}^{n-1}X_k$ for a stationary process $X=(X_n, n\in\mathbb Z)$ is studied. For a fixed $\varepsilon>0$, upper estimates for $\mathsf P\bigl(\sup_{k\ge n} |\sigma_k|\ge\varepsilon\bigr)$ as $n\to\infty$ are obtained.

UDC: 519

Received: 01.09.1997

DOI: 10.4213/mzm1406

 English version: Mathematical Notes, 1998, 64:3, 316–321

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