Limit theorems for extremes of strongly dependent cyclo-stationary χ-processes
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In this paper, with motivation from the paper of Konstant et al. (Lith Math J 44:196-208, 2004) we derive limit theorems for the maximum of strongly dependent cyclo-stationary \(\chi \)-processes. Further, under a global Hölder condition we show that Seleznjev pth-mean convergence theorem holds.
KeywordsGaussian process Cyclo-stationary process \(\chi\)-process Gumbel limit law Limit theorem Seleznjev pth-mean convergence theorem Piterbarg inequality
AMS 2000 Subject ClassificationsPrimary—60F05; Secondary—60G15
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