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Extremes of space-time Gaussian processes

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  • Kabluchko, Zakhar

Abstract

Let be a space-time Gaussian process which is stationary in the time variable t. We study Mn(h)=supt[set membership, variant][0,n]Zt(snh), the supremum of Z taken over t[set membership, variant][0,n] and rescaled by a properly chosen sequence sn-->0. Under appropriate conditions on Z, we show that for some normalizing sequence bn-->[infinity], the process bn(Mn-bn) converges as n-->[infinity] to a stationary max-stable process of Brown-Resnick type. Using strong approximation, we derive an analogous result for the empirical process.

Suggested Citation

  • Kabluchko, Zakhar, 2009. "Extremes of space-time Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3962-3980, November.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3962-3980
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    References listed on IDEAS

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    2. Davis, Richard A. & Mikosch, Thomas, 2008. "Extreme value theory for space-time processes with heavy-tailed distributions," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 560-584, April.
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    5. Hsing, Tailen, 1989. "Extreme value theory for multivariate stationary sequences," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 274-291, May.
    6. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    Cited by:

    1. Padoan, Simone A. & Bevilacqua, Moreno, 2015. "Analysis of Random Fields Using CompRandFld," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i09).
    2. Richard A. Davis & Claudia Klüppelberg & Christina Steinkohl, 2013. "Statistical inference for max-stable processes in space and time," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 791-819, November.
    3. Wang, Yizao, 2018. "Extremes of q-Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2979-3005.

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