The almost sure central limit theorems for the maxima of sums under some new weak dependence assumptions

Abstract

We prove the almost sure central limit theorems for the maxima of partial sums of r.v.’s under a general condition of dependence due to Doukhan and Louhichi. We will separately consider the centered sequences and the sequences with positive expected values.

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Correspondence to Marcin Dudziński.

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Dudziński, M., Górka, P. The almost sure central limit theorems for the maxima of sums under some new weak dependence assumptions. Acta. Math. Sin.-English Ser. 29, 429–448 (2013). https://doi.org/10.1007/s10114-013-1388-9

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Keywords

  • Almost sure central limit theorem
  • new weakly dependent random variables
  • maxima of partial sums
  • Markov chains

MR(2010) Subject Classification

  • 60F15
  • 60F05