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On the large deviation principle for the almost sure CLT

Author

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  • Lifshits, M. A.
  • Stankevich, E. S.

Abstract

Let Sk be the kth partial sum of real-valued i.i.d. random variables X1, X2,... . Define the random "empirical" measures with logarithmic weightsIf EX1m 0, then Qn satisfies strong large deviations principle, as Heck (Stochastic. Process. Appl. 76 (1998) 61), March and Seppäläinen (J. Theoret. Probab. 10 (1997) 935) have recently proved. We show that the moment assumptions are optimal in this statement.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:3:p:263-267
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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. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.
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    Cited by:

    1. 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.
    2. 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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