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.
Citation:
M. S. Muminov, “On approximating the probability of a large excursion of a nonstationary Gaussian process”, Sibirsk. Mat. Zh., 51:1 (2010), 175–195; Siberian Math. J., 51:1 (2010), 144–161
\Bibitem{Mum10}
\by M.~S.~Muminov
\paper On approximating the probability of a~large excursion of a~nonstationary Gaussian process
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
\issue 1
\pages 175--195
\mathnet{http://mi.mathnet.ru/smj2075}
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\transl
\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 1
\pages 144--161
\crossref{https://doi.org/10.1007/s11202-010-0015-6}
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Linking options:
https://www.mathnet.ru/eng/smj2075
https://www.mathnet.ru/eng/smj/v51/i1/p175
This publication is cited in the following 3 articles:
Mukhammadjon S. Muminov, Khaliq S. Soatov, “Strong Consistency of the Spline-Estimation of Probabilities Density in Uniform Metric”, OJS, 06:02 (2016), 373
Mukhammadjon S. Muminov, Kholiqjon S. Soatov, “On the Approximation of Maximum Deviation Spline Estimation of the Probability Density Gaussian Process”, OJS, 05:04 (2015), 334
Muhanmadjon S. Muminov, Kh. Soatov, “A Note on Spline Estimator of Unknown Probability Density Function”, OJS, 01:03 (2011), 157
Citation in format AMSBIB
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