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Between local and global logarithmic averages

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  • Berkes, István
  • Horváth, Lajos

Abstract

We obtain an approximation for the logarithmic averages of I{k1/2a(k) [less-than-or-equals, slant] S(k) [less-than-or-equals, slant] k1/2b(k)}, where a(k) --> 0, b(k) --> 0 (k --> [infinity]) and S(k) is partial sum of independent, identically distributed random variables.

Suggested Citation

  • Berkes, István & Horváth, Lajos, 1996. "Between local and global logarithmic averages," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 369-378, November.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:4:p:369-378
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    References listed on IDEAS

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    1. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    2. Horvath, Lajos & Khoshnevisan, Davar, 1995. "Weight functions and pathwise local central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 105-123, September.
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    Cited by:

    1. István Berkes & Lajos Horváth, 1999. "Limit Theorems for Logarithmic Averages of Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 12(4), pages 985-1009, October.

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