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Almost sure limit theorems for the maximum of stationary Gaussian sequences

Author

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  • Csáki, Endre
  • Gonchigdanzan, Khurelbaatar

Abstract

We prove an almost sure limit theorem for the maxima of stationary Gaussian sequences with covariance rn under the condition rn log n(loglog n)1+[var epsilon]=O(1).

Suggested Citation

  • Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
  • Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:195-203
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    References listed on IDEAS

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    1. 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.
    2. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
    3. Berkes, István & Horváth, Lajos, 2001. "The logarithmic average of sample extremes is asymptotically normal," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 77-98, January.
    4. 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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    Citations

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    Cited by:

    1. Dudzinski, Marcin, 2008. "The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 347-357, March.
    2. Moon, Hee-Jin & Choi, Yong-Kab, 2007. "Asymptotic properties for partial sum processes of a Gaussian random field," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 9-18, January.
    3. Hashorva, Enkelejd & Weng, Zhichao, 2013. "Limit laws for extremes of dependent stationary Gaussian arrays," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 320-330.
    4. Chen, Shouquan & Lin, Zhengyan, 2006. "Almost sure max-limits for nonstationary Gaussian sequence," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1175-1184, June.
    5. Tan, Zhongquan, 2013. "An almost sure limit theorem for the maxima of smooth stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2135-2141.
    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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