Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function

Zatula, D. V.

doi:10.17721/1812-5409.2020/1-2.3

Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function

Тип публікації :

Стаття

Дата випуску :

2020

Автор(и) :

Zatula, D. V.

Мова основного тексту :

Англійська

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/26140

DOI :

10.17721/1812-5409.2020/1-2.3

Журнал :

Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics

Випуск :

1

ISSN :

1812-5409

Початкова сторінка :

25

Кінцева сторінка :

30

Цитування :

[APA 7] Zatula, D. V. (2020). Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 25–30. https://doi.org/10.17721/1812-5409.2020/1-2.3

[ДСТУ] Zatula D. V. Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2020. no. 1. P. 25—30. DOI: 10.17721/1812-5409.2020/1-2.3 (date of access: 25.07.2026).

Complex random variables and processes with a vanishing pseudo-correlation are called proper. There is a class of stationary proper complex random processes that have a stable correlation function. In the present article we consider real stationary Gaussian processes with a stable correlation function. It is shown that the trajectories of stationary Gaussian proper complex random processes with zero mean belong to the Orlich space generated by the function $U(x) = e^{x^2/2}-1$. Estimates are obtained for the distribution of semi-norms of sample functions of Gaussian proper complex random processes with a stable correlation function, defined on the compact $\mathbb{T} = [0,T]$, in Hölder spaces.Key words: stationary Gaussian processes, proper complex random processes, Orlicz spaces, moduli of continuity, Hölder semi-norms.Pages of the article in the issue: 25 - 30Language of the article: Ukrainian

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Завантажити

Формат :

Adobe PDF

Розмір :

1.5 MB

Контрольна сума :

(MD5):3558f6fbc06fda78379c99f30d25ea16

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