Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions - Hopkalo, O. M.; Sakhno, L. M.; Vasylyk, O. I. (Київський національний університет імені Тараса Шевченка, 2020)
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