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

  • Dabrowski A
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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.

Author-supplied keywords

  • Almost sure invariance principles
  • approximation theorems
  • mixing random variables

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  • AndréRobert Dabrowski

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