Some properties and estimates for ?-sub-Gaussian stochastic processes

O. I. Vasylyk; O. M. Hopkalo; Yu. V. Kozachenko; L. M. Sakhno

doi:10.17721/1812-5409.2019/4.3

Some properties and estimates for ?-sub-Gaussian stochastic processes

Authors

O. I. Vasylyk Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-0880-3751
O. M. Hopkalo Taras Shevchenko National University of Kyiv
Yu. V. Kozachenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0001-6996-8368
L. M. Sakhno Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2019/4.3

Keywords:

φ-sub-Gaussian processes, continuity, boundedness, distribution of supremum

Abstract

In this paper, there are studied properties of stochastic processes belonging to the spaces of ?-sub-Gaussian random variables Sub_? (?). For the processes defined on R, we obtain conditions for boundedness and continuity with probability 1, estimates for the distribution of the supremum are also derived.

Pages of the article in the issue: 18 - 22

Language of the article: Ukrainian

References

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VASYLYK, O. I., KOZACHENKO, YU. V., YAMNENKO, R. E. (2008) φ-sub-Gaussian random process, Kyiv: Vydavnycho-Poligrafichnyi Tsentr “Kyivskyi Universytet”, 231 p. (In Ukrainian)

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HOPKALO, О.М. (2018) Conditions for boundedness of a Gaussian stochastic process with probability 1 on R+ and their application // Bulletin of Uzhgorod University. Series: Mathematics and Informatics. Iss.2, p. 61–69.

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Published

2020-02-12

Issue

No. 4 (2019)

Section

Algebra, Geometry and Probability Theory

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How to Cite

Vasylyk, O. I., Hopkalo, O. M., Kozachenko, Y. V., & Sakhno, L. M. (2020). Some properties and estimates for ?-sub-Gaussian stochastic processes. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, 4, 18-22. https://doi.org/10.17721/1812-5409.2019/4.3