This article is cited in 3 papers

On approximating the probability of a large excursion of a nonstationary Gaussian process

M. S. Muminov

Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Abstract: We consider a nonstationary Gaussian process with the zero mean and unit variance which possesses the mean square derivative. We study the asymptotic behavior of the maximum Gaussian processes on both finite and increasing intervals. The results are applied to studying the maximal deviation of empirical density and the regression curve on a finite interval.

Keywords: nonstationary Gaussian process, asymptotic behavior, maximum distributions, level crossing, factorial moments, mean square derivatives.

UDC: 519.21

Received: 07.05.2008
Revised: 21.05.2009

 English version: Siberian Mathematical Journal, 2010, 51:1, 144–161

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