Decrease rate of the probabilities of \(\varepsilon\)-deviations for the means of stationary processes
type: Item
instance of: scholarly article
title: Decrease rate of the probabilities of \(\varepsilon\)-deviations for the means of stationary processes
zbMATH Open document ID: 0930.60027
DOI: 10.1007/BF02314839
published in: Mathematical Notes
publication date: 2000-01-31T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 1294969
zbMATH Keywords: arithmetic means of stationary processes
zbMATH Keywords: probability of deviation
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: stochastic spectral measure
author: V. F. Gaposhkin
reviewed by: Andriy Olenko
MaRDI profile type: Publication
cites work: Q3994694
cites work: Q4057867
cites work: Q3933708
cites work: The rate of convergence in ergodic theorems
cites work: Q3254471
description: scientific article; zbMATH DE number 1294969