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A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process. / Miroshin, R.N.

In: Vestnik St. Petersburg University: Mathematics, No. 3, 2014, p. 115-122.

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Harvard

Miroshin, RN 2014, 'A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process', Vestnik St. Petersburg University: Mathematics, no. 3, pp. 115-122. https://doi.org/10.3103/S1063454114030054

APA

Miroshin, R. N. (2014). A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process. Vestnik St. Petersburg University: Mathematics, (3), 115-122. https://doi.org/10.3103/S1063454114030054

Vancouver

Miroshin RN. A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process. Vestnik St. Petersburg University: Mathematics. 2014;(3):115-122. https://doi.org/10.3103/S1063454114030054

Author

Miroshin, R.N. / A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process. In: Vestnik St. Petersburg University: Mathematics. 2014 ; No. 3. pp. 115-122.

BibTeX

@article{97f323ee76fa40ba838af50afd75c3d0,
title = "A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process",
abstract = "{\textcopyright} Allerton Press, Inc., 2014. The variance of the number of zeros of a Gaussian differentiable stationary process in a finite time interval can be represented by a single integral of a sophisticated function having singularities in the vicinity of zero, which complicates computer calculations. In this paper, for a wide class of correlation functions, an inequality estimating this variance in simpler terms is proved. Two of three considered examples demonstrate the limits of the effectiveness of the obtained inequality by comparison with special processes earlier established by the author for which the variance is calculated by formulas without integrals. In the two subsequent cases, the inequality is used for the asymptotic estimation of the variance of the number of zeros in a small time interval and, in the last one, in addition to this asymptotics, the upper and lower bounds for the most widely used analytic process in all time intervals.",
author = "R.N. Miroshin",
year = "2014",
doi = "10.3103/S1063454114030054",
language = "English",
pages = "115--122",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - A simple inequality for the variance of the number of zeros of a differentiable gaussian stationary process

AU - Miroshin, R.N.

PY - 2014

Y1 - 2014

N2 - © Allerton Press, Inc., 2014. The variance of the number of zeros of a Gaussian differentiable stationary process in a finite time interval can be represented by a single integral of a sophisticated function having singularities in the vicinity of zero, which complicates computer calculations. In this paper, for a wide class of correlation functions, an inequality estimating this variance in simpler terms is proved. Two of three considered examples demonstrate the limits of the effectiveness of the obtained inequality by comparison with special processes earlier established by the author for which the variance is calculated by formulas without integrals. In the two subsequent cases, the inequality is used for the asymptotic estimation of the variance of the number of zeros in a small time interval and, in the last one, in addition to this asymptotics, the upper and lower bounds for the most widely used analytic process in all time intervals.

AB - © Allerton Press, Inc., 2014. The variance of the number of zeros of a Gaussian differentiable stationary process in a finite time interval can be represented by a single integral of a sophisticated function having singularities in the vicinity of zero, which complicates computer calculations. In this paper, for a wide class of correlation functions, an inequality estimating this variance in simpler terms is proved. Two of three considered examples demonstrate the limits of the effectiveness of the obtained inequality by comparison with special processes earlier established by the author for which the variance is calculated by formulas without integrals. In the two subsequent cases, the inequality is used for the asymptotic estimation of the variance of the number of zeros in a small time interval and, in the last one, in addition to this asymptotics, the upper and lower bounds for the most widely used analytic process in all time intervals.

U2 - 10.3103/S1063454114030054

DO - 10.3103/S1063454114030054

M3 - Article

SP - 115

EP - 122

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 7063219