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Extremes of \(\alpha(\mathbf{t})\)-locally stationary Gaussian random fields. (English) Zbl 1408.60041

Summary: The main result of this contribution is the derivation of the exact asymptotic behavior of the supremum of a class of \(\alpha (\mathbf{t})\)-locally stationary Gaussian random fields. We present two applications of our result: the first one deals with the extremes of aggregate multifractional Brownian motions, whereas the second one establishes the exact asymptotics of the supremum of the \(\chi\)-process generated by multifractional Brownian motions.

MSC:

60G70 Extreme value theory; extremal stochastic processes
60G60 Random fields
60G15 Gaussian processes
60G10 Stationary stochastic processes
60G22 Fractional processes, including fractional Brownian motion
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