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Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise. / Baluev, R. V.; Topinskiy, V. V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 58, No. 3, 06.08.2025, p. 370-378.

Research output: Contribution to journal › Article › peer-review

Harvard

Baluev, RV & Topinskiy, VV 2025, 'Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise', Vestnik St. Petersburg University: Mathematics, vol. 58, no. 3, pp. 370-378. https://doi.org/10.1134/s1063454125700360

APA

Baluev, R. V., & Topinskiy, V. V. (2025). Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise. Vestnik St. Petersburg University: Mathematics, 58(3), 370-378. https://doi.org/10.1134/s1063454125700360

Vancouver

Baluev RV, Topinskiy VV. Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise. Vestnik St. Petersburg University: Mathematics. 2025 Aug 6;58(3):370-378. https://doi.org/10.1134/s1063454125700360

Author

Baluev, R. V. ; Topinskiy, V. V. / Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise. In: Vestnik St. Petersburg University: Mathematics. 2025 ; Vol. 58, No. 3. pp. 370-378.

BibTeX

@article{dcb89fdc87a14e5e9e8188ac523d03a5,
title = "Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise",
abstract = "Abstract: In this work, an explicit expression is obtained for the distribution function of a centered and normalized data vector containing a deterministic signal (or without a signal) and Gaussian white noise with constant variance. The obtained representation is exact and does not rely on any asymptotics for a large number of observations in particular; it is ultimately expressed through an error function and elementary functions and requires iterative calculations based on a recurrence formula.",
keywords = "data centering, data normalization, discrete white noise, multivariate density distribution, signal detection",
author = "Baluev, {R. V.} and Topinskiy, {V. V.}",
year = "2025",
month = aug,
day = "6",
doi = "10.1134/s1063454125700360",
language = "English",
volume = "58",
pages = "370--378",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Multivariate Distribution Function for a Centered and Normalized Time Series with Gaussian White Noise

AU - Baluev, R. V.

AU - Topinskiy, V. V.

PY - 2025/8/6

Y1 - 2025/8/6

N2 - Abstract: In this work, an explicit expression is obtained for the distribution function of a centered and normalized data vector containing a deterministic signal (or without a signal) and Gaussian white noise with constant variance. The obtained representation is exact and does not rely on any asymptotics for a large number of observations in particular; it is ultimately expressed through an error function and elementary functions and requires iterative calculations based on a recurrence formula.

AB - Abstract: In this work, an explicit expression is obtained for the distribution function of a centered and normalized data vector containing a deterministic signal (or without a signal) and Gaussian white noise with constant variance. The obtained representation is exact and does not rely on any asymptotics for a large number of observations in particular; it is ultimately expressed through an error function and elementary functions and requires iterative calculations based on a recurrence formula.

KW - data centering

KW - data normalization

KW - discrete white noise

KW - multivariate density distribution

KW - signal detection

UR - https://www.mendeley.com/catalogue/34b3cede-7a4a-3f07-a8b5-8c7eec9990d7/

U2 - 10.1134/s1063454125700360

DO - 10.1134/s1063454125700360

M3 - Article

VL - 58

SP - 370

EP - 378

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 141514904