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Large deviations for some logarithmic means in the case of random variables with thin tails

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  • Giuliano, Rita
  • Macci, Claudio

Abstract

In this paper we generalize Theorem 3.3 in Giuliano and Macci (2011). More precisely we prove the full large deviation principle without assuming a particular condition in that theorem and, moreover, we give some results for the case of random variables with thin tails (and not super-exponential tails). As an application we deduce some consequences for the logarithmic means of some random variables expressed in terms of a C-process.

Suggested Citation

  • Giuliano, Rita & Macci, Claudio, 2018. "Large deviations for some logarithmic means in the case of random variables with thin tails," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 47-56.
  • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:47-56
    DOI: 10.1016/j.spl.2018.02.066
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    References listed on IDEAS

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    1. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
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    3. Berkes, István & Csáki, Endre, 2001. "A universal result in almost sure central limit theory," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 105-134, July.
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    5. Lifshits, M. A. & Stankevich, E. S., 2001. "On the large deviation principle for the almost sure CLT," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 263-267, February.
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    Cited by:

    1. Giuliano, Rita & Macci, Claudio & Pacchiarotti, Barbara, 2019. "Large deviations for weighted means of random vectors defined in terms of suitable Lévy processes," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 13-22.

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