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A law of the iterated logarithm for extreme values from Gaussian sequences. (English) Zbl 0387.60035

MSC:
60F15 Strong limit theorems
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[1] Deo, C.M.: An iterated logarithm law for maxima of non-stationary Gaussian processes. J. Appl. Probability 10, 402-408 (1973) · Zbl 0273.60018 · doi:10.2307/3212356
[2] LePage, R.D.: Loglog law for Gaussian processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 25, 103-108 (1973) · Zbl 0237.60017 · doi:10.1007/BF00533098
[3] Mittal, Y.: Limiting behaviour of maxima in stationary Gaussian sequences. Ann. Probability 2, 231-242 (1974) · Zbl 0279.60025 · doi:10.1214/aop/1176996705
[4] Pakshirajan, R.P., Vasudeva, R.: A law of the iterated logarithm for stable summands. Trans. Amer. Math. Soc. 232, 33-42 (1977) · Zbl 0325.60034 · doi:10.1090/S0002-9947-1977-0455093-4
[5] Pickands, J. III: An iterated logarithm law for the maximum in a stationary Gaussian sequence. Z. Wahrscheinlichkeitstheorie verw. Gebiete 12, 344-353 (1969) · Zbl 0181.20703 · doi:10.1007/BF00538755
[6] Qualls, C., Watanabe, H.: An asymptotic 0-1 behaviour of Gaussian process. Ann. Math. Statist. 42, 2029-2035 (1971) · Zbl 0239.60031 · doi:10.1214/aoms/1177693070
[7] Strassen, V.: An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie verw. Gebiete 3, 211-226 (1964) · Zbl 0132.12903 · doi:10.1007/BF00534910
[8] Vishnu Hebbar, H.: Almost sure limit points of maxima of stationary Gaussian sequences. [Submitted to Ann. Probability] · Zbl 0428.60041
[9] Welsch, R. E.: A weak convergence theorem for order statistics from strong-mixing processes. Ann. Math. Statist. 42, 1637-1646 (1971) · Zbl 0244.60008 · doi:10.1214/aoms/1177693162
[10] Welsch, R.E.: A convergence theorem for extreme values from Gaussian sequences. Ann. Probability 1, 398-404 (1973) · Zbl 0258.62030 · doi:10.1214/aop/1176996934
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