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An extension of the almost sure max-limit theorem

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  • Fahrner, Ingo

Abstract

We extend the almost sure max-limit theorem to the case of unbounded functions.

Suggested Citation

  • Fahrner, Ingo, 2000. "An extension of the almost sure max-limit theorem," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 93-103, August.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:1:p:93-103
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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.
    2. Berkes, István & Csáki, Endre & Horváth, Lajos, 1998. "Almost sure central limit theorems under minimal conditions," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 67-76, January.
    3. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
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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. Stadtmüller, U., 2002. "Almost sure versions of distributional limit theorems for certain order statistics," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 413-426, July.
    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. Fahrner, Ingo, 2001. "A strong invariance principle for the logarithmic average of sample maxima," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 317-337, June.
    5. Chen, Shouquan & Lin, Zhengyan, 2006. "Almost sure max-limits for nonstationary Gaussian sequence," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1175-1184, June.
    6. Tan, Zhongquan & Peng, Zuoxiang, 2009. "Almost sure convergence for non-stationary random sequences," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 857-863, April.

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