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High excursions for nonstationary generalized chi-square processes. (English) Zbl 0815.60045
Let \(X(t)\), \(t \in [0,T]\), be a centered differentiable Gaussian random process and let \(X_ 1(t),\dots\), \(X_ n(t)\) be independent copies of \(X(t)\). Assume that the variance of the process \(X(t)\) attains its global maximum in only one inner point of the interval \([0,T]\). The author investigates an exact asymptotic behavior of large deviation probabilities for the generalized chi-square process \(\chi^ 2_ b(t) = \sum^ n_{i = 1} b^ 2_ i X^ 2_ i(t)\), where \(b_ 1,b_ 2,\dots,b_ n\) are positive constants. The paper uses asymptotic methods for the investigation of large deviation probabilities of Gaussian processes and fields, especially the so-called “double sum method” of the author [Asymptotic methods in the theory of Gaussian stochastic processes and fields (1988; Zbl 0652.60045)].

MSC:
60G70 Extreme value theory; extremal stochastic processes
60G60 Random fields
60F10 Large deviations
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