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

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

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