Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions
Тип публікації :
Стаття
Дата випуску :
2020
Автор(и) :
Hopkalo, O. M.
Sakhno, L. M.
Vasylyk, O. I.
Мова основного тексту :
Англійська
eKNUTSHIR URL :
Випуск :
1
ISSN :
1812-5409
Початкова сторінка :
17
Кінцева сторінка :
24
Цитування :
[APA 7] Hopkalo, O. M., Sakhno, L. M., & Vasylyk, O. I. (2020). Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 17–24. https://doi.org/10.17721/1812-5409.2020/1-2.2
[ДСТУ] Hopkalo O. M., Sakhno L. M., Vasylyk O. I. Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2020. no. 1. P. 17—24. DOI: 10.17721/1812-5409.2020/1-2.2 (date of access: 25.07.2026).
In this paper, there are studied sample paths properties of stochastic processes representing solutions (in $L_2(\Omega)$ sense) of the heat equation with random initial conditions given by $\varphi$-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded and unbounded domains.Key words: ?-sub-Gaussian processes, heat equation, random initial condition, distribution of supremum.Pages of the article in the issue: 17 - 24Language of the article: English
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