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Logarithmic averages of stable random variables are asymptotically normal

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  • Berkes, István
  • Horváth, Lajos
  • Khoshnevisan, Davar

Abstract

We show that most random walks in the domain of attraction of a symmetric stable law have a non-trivial almost sure central limit theorem with the normal law as the limit.

Suggested Citation

  • Berkes, István & Horváth, Lajos & Khoshnevisan, Davar, 1998. "Logarithmic averages of stable random variables are asymptotically normal," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 35-51, September.
    • Handle: RePEc:eee:spapps:v:77:y:1998:i:1:p:35-51
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    References listed on IDEAS

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    1. 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. Berkes, István & Horváth, Lajos, 2001. "The logarithmic average of sample extremes is asymptotically normal," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 77-98, January.

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