Decrease rate of the probabilities of \(\varepsilon\)-deviations for the means of stationary processes
The author considers a second-order stationary process \((X_n, n\in Z).\) The behavior of the arithmetic means \(\sigma_n= {{1}\over{n}}\sum_{k=0}^{n-1}X_k\) as \(n \to \infty\) is studied. Under conditions on variances of \(\{\sigma_n\}\) the author obtains estimates for \(P(\sup_{k\geq n}|\sigma_k|\geq \varepsilon), \;n \to \infty.\) Different corollaries are considered.
arithmetic means of stationary processes
scientific article; zbMATH DE number 1294969