Investigation of Airy equations with random initial conditions

Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

“…We present the proof for the cases of metrics d 2 and d 3 , other cases are treated similarly. Note that the bound for the case of d 1 was stated in Sakhno (2023b).…”

“…The mean-square solution can be written in the following form (see, Sakhno (2023b) and references therein):…”

“…Theorem 1.2 with a particular metric space (T, d) has been applied in Hopkalo and Sakhno (2021); Kozachenko et al (2020); Sakhno (2023b) for studying solutions to partial differential equations with random initial condition, in Sakhno (2023a) for evaluation of suprema of spherical random fields, in Kozachenko and Olenko (2016) for developing uniform approximation schemes for ϕ-sub-Gaussian processes. This theorem allows to calculate the bounds for the distribution of suprema in the closed form.…”