A note on a theorem of Berkes and Philipp for dependent sequences

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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{lunate})(1 + 2/δ) and the undetermined quantities aNare replaced by Nσ2for some σ > 0. © 1982.

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Dabrowski, A. (1982). A note on a theorem of Berkes and Philipp for dependent sequences. Statistics and Probability Letters, 1(2), 53–55. https://doi.org/10.1016/0167-7152(82)90015-3

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