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On the logarithmic average of additive functionals

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  • Csáki, E.
  • Földes, A.

Abstract

Let X1, X2, ... be i.i.d. integer valued random variables, put Sn = X1 + ... + Xn. Let f(x) be a real valued function on integers with . We establish functional central limit theorem for the logarithmic average of the additive functionals An = [Sigma]k=1nf(Sk). Similar results are also given for additive functionals of the Wiener process.

Suggested Citation

  • Csáki, E. & Földes, A., 1995. "On the logarithmic average of additive functionals," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 261-268, March.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:4:p:261-268
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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.
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