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

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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.

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Authors and Affiliations

  1. Mathematics and Information Technology Institute, Tashkent, Uzbekistan

    M. S. Muminov

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  1. M. S. Muminov
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Correspondence to M. S. Muminov.

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Original Russian Text Copyright © 2010 Muminov M. S.

Tashkent. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 1, pp. 175–195, January–February, 2010.

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Muminov, M.S. On approximating the probability of a large excursion of a nonstationary Gaussian process. Sib Math J 51, 144–161 (2010). https://doi.org/10.1007/s11202-010-0015-6

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  • DOI: https://doi.org/10.1007/s11202-010-0015-6

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