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The principle of large deviations for the almost everywhere central limit theorem

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  • Heck, Matthias K.

Abstract

The purpose of the present paper is to prove a principle of large deviations for Brosamler's functional almost everywhere central limit theorem for i.i.d. random variables on . This principle of large deviations for the functional almost everywhere central limit theorem naturally implies a principle of large deviations for Brosamler and Schatte's almost everywhere central limit theorem. Furthermore it implies principles of large deviations for various other almost everywhere limit theorems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:76:y:1998:i:1:p:61-75
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    References listed on IDEAS

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    1. Bryc, Wlodzimierz & Dembo, Amir, 1995. "On large deviations of empirical measures for stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 23-34, July.
    2. 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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    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. Kifer, Yuri, 2013. "Strong approximations for nonconventional sums and almost sure limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2286-2302.
    3. 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.
    4. 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.
    5. Alain Rouault & Marc Yor & Marguerite Zani, 2002. "A Large Deviations Principle Related to the Strong Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 15(3), pages 793-815, July.

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