Mathematical Notes

, Volume 68, Issue 4, pp 444–451 | Cite as

Refinement of the almost sure central limit theorem for associated processes

  • M. A. Vronskii


In this paper, for the partial sumsS n of a stationary associated random process it is proved that the logarithmic averages\((\log n)^{ - 1} \sum\nolimits_{j = 1}^n {f(S_j /\sqrt j )/j} \) converge almost surely. The asymptotic normality of the normalized difference between the logarithmic averages and their limiting value is established.

Key words

associated random variables central limit theorem almost sure versions of limit theorems 


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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • M. A. Vronskii
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowUSSR

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