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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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##### References:
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