A note on a theorem of Berkes and Philipp for dependent sequences |
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| Authors: | AndrRobert Dabrowski |
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| Institution: | Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada |
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| Abstract: | We improve an almost sure invariance principle for f-mixing sequences of real random variables with finite (2 + δ)th moment (0 < δ 2) due to Berkes and Philipp (1979). The exponent of the slow logarithmic rate of mixing in that theorem is relaxed from 160/δ to (1 + ε)(1 + 2/δ) and the undetermined quantities aN are replaced by Nσ2 for some σ > 0. |
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| Keywords: | Almost sure invariance principles mixing random variables approximation theorems |
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