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Decrease rate of the probabilities ofε-deviations for the means of stationary processes |
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| Authors: | V F Gaposhkin |
| Institution: | (1) Moscow State Communication Lines University, USSR |
| Abstract: | The asymptotic behavior asn → ∞ of the normed sumsσn =n −1 Σ k =0n−1 Xk for a stationary processX = (X n ,n ∈ ℤ) is studied. For a fixedε > 0, upper estimates for P(sup k≥n |σ k | ≥ε) asn → ∞ are obtained. Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 366–372, September, 1998. |
| Keywords: | arithmetic means of stationary processes probability of deviation strong law of large numbers stochastic spectral measure |
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